FINITE INTEGRAL RELATION ALGEBRAS
ROGER D. MADDUX
1. Nonexistence
Please note that this paper does not exist. It consists entirely of excerpts from the
forthcoming book Relation Algebras, Studies in Logic, Vol. 150, Elsevier, scheduled
for publication in July 2006. Consequently any reference to this (nonexistent) paper
should instead be directed to the book.
2. Cycles in structures
The method of forming complex algebras of finite ternary relations will produce
all finite nonassociative relation algebras. We use this method to construct many
interesting algebras. Every atomic NA determines an involution on atoms, which
in turn determines both the cycles of the algebra and also the missing, or forbidden
cycles. So we begin by studying the cycles of an arbitrary involution.
˘ = u for all u ∈ U .
Suppose ˘ is an involution on U , that is, ˘ : U → U and ŭ
For any x, y, z ∈ U let
[x, y, z]˘ = {hx, y, zi , hx̆, z, yi , hy, z̆, x̆i , hy̆, x̆, z̆i , hz̆, x, y̆i , hz, y̆, xi}.
The set [x, y, z]˘ is called a ˘-cycle, or simply a cycle in case the involution may
be deduced from the context. Notice that [x, y, z]˘ is the closure of {hx, y, zi} under
these two involutions on U 3 :
f1 := hx̆, z, yi : hx, y, zi ∈ U 3 ,
f2 := hz, y̆, xi : hx, y, zi ∈ U 3 .
Furthermore, every triple in [x, y, z]˘ generates [x, y, z]˘ using f1 and f2 :
ha, b, ci ∈ [x, y, z]˘ ⇔ [a, b, c]˘ = [x, y, z]˘.
It follows that, for all a, b, c, x, y, z ∈ U , the cycles [a, b, c]˘ and [x, y, z]˘ are either
identical or disjoint. A cycle can be classified according to various criteria, such
as the cardinality of {x, y, z}, whether x is symmetric (x = x̆) or asymmetric
(x · x̆ = 0), etc. We regard two cycles as having the same type if there is a
permutation of U that preserves ˘ and carries one cycle into the other. In more
detail, if p−1 |p = p|p−1 = U 1 and p|˘ = ˘|p, then [x, y, z](p|˘) is the same type of
cycle as [x, y, z]˘. It turns out that there are 13 types of cycles. These types are
illustrated below under these assumptions:
a, b, c, q, q̆, r, r̆, s, s̆ ∈ U,
{a, b, c, q, q̆, r, r̆, s, s̆} = 9.
Date: 10 February 2006.
1991 Mathematics Subject Classification. Primary: 03G15.
1
2
ROGER D. MADDUX
The notation used in these assumptions determines the action of ˘ on the atoms a,
b, c, q, q̆, r, r̆, s, and s̆. Note that every type of cycle has cardinality 1, 2, 3, or 6.
(1)
[a, a, a]˘ = {ha, a, ai},
(2)
[r, r, r̆ ]˘ = {hr, r, r̆i , hr̆, r̆, ri},
(3)
[a, b, b]˘ = {hb, a, bi , hb, b, ai , ha, b, bi},
(4)
[r, a, r ]˘ = {hr, a, ri , hr̆, r, ai , ha, r̆, r̆i},
(5)
[a, b, c]˘ = {ha, b, ci , ha, c, bi , hb, c, ai , hb, a, ci , hc, a, bi , hc, b, ai},
(6)
[r, a, a]˘ = {hr, a, ai , hr̆, a, ai , ha, a, r̆i , ha, r̆, ai , ha, r, ai , ha, a, ri},
(7)
[r, a, b]˘ = {hr, a, bi , hr̆, b, ai , ha, b, r̆i , ha, r̆, bi , hb, r, ai , hb, a, ri},
(8)
[r, r, a]˘ = {hr, r, ai , hr̆, a, ri , hr, a, r̆i , hr̆, r̆, ai , ha, r, r̆i , ha, r̆, ri},
(9)
[r, s, a]˘ = {hr, s, ai , hr̆, a, si , hs, a, r̆i , hs̆, r̆, ai , ha, r, s̆i , ha, s̆, ri},
(10)
[r, r, r ]˘ = {hr, r, ri , hr̆, r, ri , hr, r̆, r̆i , hr̆, r̆, r̆i , hr̆, r, r̆i , hr, r̆, ri},
(11)
[r, r, s]˘ = {hr, r, si , hr̆, s, ri , hr, s̆, r̆i , hr̆, r̆, s̆i , hs̆, r, r̆i , hs, r̆, ri},
(12)
[r, s, r ]˘ = {hr, s, ri , hr̆, r, si , hs, r̆, r̆i , hs̆, r̆, r̆i , hr̆, r, s̆i , hr, s̆, ri},
(13)
[r, s, q ]˘ = {hr, s, qi , hr̆, q, si , hs, q̆, r̆i , hs̆, r̆, q̆i , hq̆, r, s̆i , hq, s̆, ri}.
We use some special terminology when dealing with cycles whose atoms are all
symmetric. Cycles of type (1) are called 1-cycle, cycles of type (3) are called
2-cycle, and cycles of type (5) are called 3-cycle.
Although the involution ˘ determines the cycles it does not, by itself, determine
the identity element. To see this, suppose that ˘ arises from a ternary relation T
on U whose complex algebra is in NA. This means that
(i) T is a ternary relation on U , i.e., T ⊆ U 3 ,
(ii) the field of T is U ,
(iii) T is consistent with ˘,
(iv) Cm (T ) ∈ NA.
Let I be I is the identity element of the complex algebra Cm (T ). What we can say
on the basis of these assumptions about the individual elements of I is that
(i) if i ∈ I then ĭ = i,
(ii) [i, i, i] ⊆ T and [i, i, i] is a cycle of type (1),
(iii) for every u ∈ U , if ŭ = u then [i, u, u] is a cycle of type (3) and either
[i, u, u] ⊆ T or [i, u, u] ∩ T = ∅,
(iv) for every u ∈ U , if ŭ 6= u then [u, i, u] is a cycle of type (4) and either
[u, i, u] ⊆ T or [i, u, u] ∩ T = ∅.
For any given u ∈ U , there are i, e ∈ I such that T iuu and T eŭŭ, hence [i, u, u] ∪
[e, ŭ, ŭ] ⊆ T . If ŭ = u, then i = e and [i, u, u] is a cycle of type (3). Suppose, on the
other hand, that ŭ 6= u. Then it is possible but not necessary that i 6= e. Because
[i, u, u] = [ŭ, i, ŭ] and [e, ŭ, ŭ] = [u, e, u], we see that [i, u, u] and [i, ŭ, ŭ] are cycles
of type (3).
We now survey the simplest case, in which I contains a single element. In this
case the identity element of Cm (T ) is an atom. In spite of the notational clash
,
,
thereby created, we will let 1 be the sole element of I, so we know that T 1 uu for
every u ∈ U . The clash is illustrated by the fact that we may now correctly write
,
,
,
1 = 1 Cm(T ) = {1 }.
FINITE INTEGRAL RELATION ALGEBRAS
3
Over the years several mathematicians have attempted to enumerate small finite
,
relation algebras in which 1 is an atom. This includes R. Lyndon [16, fn. 13],
F. Backer [2], R. McKenzie [19], U. Wostner [21], B. McEvoy, S. Comer [3, 13],
P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The
numbers are shown in Table 1. Lyndon found the numbers of relation algebras
with at most three atoms. Comer first computed the numbers of integral relation
algebras with exactly four atoms. The numbers of integral relation algebras with
five atoms were first computed using programs written in Pascal and run on a VAX
11/780 and a Zenith Z-100 in the 1980s. The numbers of integral relation algebras
with six atoms were computed using a very efficient program written in Pascal by
P. Jipsen and E. Lukács.
To explain the meanings of the entries, let us consider the line in Table 1 beginning with “37”. This entry tells us that there are 37 isomorphism types of relation
,
algebras in which the atoms are 1 , a, r, r̆. Note that when we construct the com,
plex algebra from T , the atoms are actually {1 }, {a}, {r}, {r̆}. For convenience
we will ignore this distinction. In the first column are listed the symmetric atoms.
,
These can be deduced by our notational convention, and are just 1 and a. The
asymmetric atoms are listed in the second column; they are r and r̆.
The number i in the fourth column is the number of identity cycles. The identity
, , ,
cycles for every one of the 37 algebras are [1 , 1 , 1 ], [i, a, a], [r, i, r], and [i, r, r]. For
,
relation algebras in which 1 is an atom, the number of identity cycles is always equal
to the number of atoms. The sixth column tells us the total number c of cycles
available, according to the structure of ˘. For the case at hand, in which every
,
algebra has atoms 1 , a, r, r̆, the available cycles are the four identity cycles listed
above, plus these seven diversity cycles: [a, a, a], [r, r, r], [r, r, r̆], [a, r, r], [r, a, r],
[r, a, a], and [r, r, a]. The number of diversity cycles, called d in the table, is given
in the fifth column. Thus we have i + d = c.
Each individual relation algebra among the 37 isomorphism types is determined
by a selection from the list of diversity cycles. To guarantee that the identity law R6
holds in Cm (T ), it is necessary and sufficient to include in T the four identity cycles
listed above. If T is the union of these required identity cycles plus some of the
seven available diversity cycles, then Cm (T ) ∈ NA. Hence the maximum number of
,
isomorphism types of nonassociative relation algebras having atoms 1 , a, r, r̆ is 27 .
Of course, many of these 128 algebras are isomorphic. The potential isomorphisms
,
must preserve ˘ and must map 1 to itself. The number aut of such maps in
Table 1 and is given in the seventh column. For nonassociative relation algebras
,
with atoms 1 , a, r, r̆ there are only two such maps, the identity map and the one
which interchanges r and r̆. Each NA formed by selecting some diversity cycles
therefore has the potential to have at most one other copy of itself among the
128 nonassociative relation algebras. Hence the number of nonassociative relation
,
algebras with atoms 1 , a, r, r̆ is at most 128 and at least 64.
,
From Table 1 we see that there are 4527 relation algebras in which 1 is an atom
and the total number of atoms is five or less. In Table 2 we have listed the identity
and diversity cycles from which each of these 4527 algebras can be created. To save
space, commas have been omitted from the notation for the cycles. Note that no
algebra with five or fewer atoms can contain three pairs of asymmetric atoms, so
none of these 4527 algebras contains a cycle of type (13). Similarly, none of these
4527 algebras contains a cycle of type (9) since that type of cycle only occurs in
4
ROGER D. MADDUX
no. in RA
1
2
3
7
37
65
83
1, 316
3, 013
47, 865
988, 464
3, 849, 920
?
?
?
?
symm.
,
1
,
1 ,a
,
1
,
1 , a, b
,
1 ,a
,
1 , a, b, c
,
1
,
1 , a, b
,
1 , a, b, c, d
,
1 ,a
,
1 , a, b, c
,
1 , a, b, c, d, e
,
1
,
1 , a, b
,
1 , a, b, c, d
,
1 , a, b, c, d, e, f
asymm.
r, r̆
r, r̆
r, r̆, s, s̆
r, r̆
r, r̆, s, s̆
r, r̆
r, r̆, s, s̆, q, q̆
r, r̆, s, s̆
r, r̆
i
1
2
3
3
4
4
5
5
5
6
6
6
7
7
7
7
d
0
1
2
4
7
10
12
16
20
25
30
35
38
44
50
56
c aut
1
1
3
1
5
2
7
2
11
2
14
6
17
8
21
4
25 24
31
8
36 12
41 120
45 48
51 16
57 48
63 720
Table 1. Numbers of types of algebras
algebras with at least six atoms. There are, altogether, 51 cycles needed for these
4527 algebras. They are shown in Table 2, grouped according to their type.
These same cycles appear again in Table 3, this time grouped according to the
lists of atoms in Table 1. For example, the two lines in Table 3 beginning with
,
the line in which 1 , a, r, r̆ appears contain the cycles needed for the creation of
,
37 relation algebras that have atoms 1 , a, r, and r̆. The first of these two lines
contains the four identity cycles that must be included for each of these algebras,
while the next line contain the seven optional diversity cycles. For each choice of
atoms, the required identity cycles appear in the first line, while the remaining lines
contain the diversity cycles.
3. Classification of simple finite algebras
Assume A ∈ RA and A is finite. Then A is a perfect extension of itself and
A∼
= A+ . Let 3 ≤ n < ω. Let Bn A be the set of those n-by-n matrices of atoms of
A which satisfy the following conditions for all i, j, k < n:
,
(14)
aii ≤ 1 ,
(15)
ăij = aji ,
(16)
aik ≤ aij ;ajk .
It is known that A ∈ RAn iff A has an n-dimensional relational basis. Since Bn A is
a finite set and an n-dimensional relational basis for A is a special sort of subset of
Bn A satisfying conditions that can be mechanically checked, it follows that there
is an algorithm for determining whether a finite RA is in RAn : just inspect each
subset of Bn A to see whether it is an n-dimensional relational basis for A. It follows
that a finite RA is in RRA iff it has an n-dimensional relational basis for every finite
n ≥ 3. This need to perform infinitely many checks suggests that there may be no
FINITE INTEGRAL RELATION ALGEBRAS
type
(1)
(3)
(4)
(1)
(10)
(2)
(3)
(4)
(6)
(8)
(11)
(12)
(5)
(7)
size no.
1
1
3
4
3
4
1
4
6
2
2
2
3 12
6
6
6
6
6
6
6
4
2
2
4
4
4
2
names
, , ,
[1 1 1 ]
,
,
,
,
[1 aa] [1 bb] [1 cc] [1 dd]
,
,
,
,
[r1 r] [1 rr] [s1 s] [1 ss]
[aaa] [bbb] [ccc] [ddd]
[rrr] [sss]
[rrr̆] [sss̆]
[abb] [baa] [acc] [caa] [add] [daa]
[bcc] [cbb] [bdd] [dbb] [cdd] [dcc]
[arr] [rar] [brr] [rbr]
[raa] [rbb]
[rra] [rrb]
[rrs] [rrs̆] [ssr] [ssr̆]
[srr] [rsr] [rss] [srs]
[abc] [abd] [acd] [bcd]
[abr] [bar]
Table 2. Cycles needed for 4527 algebras, by type
no. in RA
1
2
3
7
37
65
83
1, 316
3, 013
atoms
,
1
,
1 ,a
cycles
, , ,
[1 1 1 ]
, , , ,
[1 1 1 ] [1 aa]
[aaa]
,
, , ,
,
,
1 , r, r̆ [1 1 1 ] [r1 r] [1 rr]
[rrr] [rrr̆]
,
, , , ,
,
1 , a, b [1 1 1 ] [1 aa] [1 bb]
[aaa] [bbb] [abb] [baa]
,
, , , ,
,
,
1 , a, r, r̆ [1 1 1 ] [1 aa] [r1 r] [1 rr]
[aaa] [rrr] [rrr̆] [arr] [rar] [raa] [rra]
,
, , , ,
,
,
1 , a, b, c [1 1 1 ] [1 aa] [1 bb] [1 cc]
[aaa] [bbb] [ccc]
[abb] [baa] [acc] [caa] [bcc] [cbb] [abc]
,
, , ,
,
,
,
,
1 , r, r̆, s, s̆ [1 1 1 ] [r1 r] [1 rr] [s1 s] [1 ss]
[rrr] [sss] [rrr̆] [sss̆]
[rrs] [rrs̆] [ssr] [ssr̆] [srr] [rsr] [rss] [srs]
,
, , , ,
,
,
,
1 , a, b, r, r̆ [1 1 1 ] [1 aa] [1 bb] [r1 r] [1 rr]
[aaa] [bbb] [rrr] [rrr̆]
[abb] [baa] [arr] [rar] [brr] [rbr]
[raa] [rbb] [rra] [rrb] [abr] [bar]
,
, , , ,
,
,
,
1 , a, b, c, d [1 1 1 ] [1 aa] [1 bb] [1 cc] [1 dd]
[aaa] [bbb] [ccc] [ddd]
[abb] [baa] [acc] [caa] [add] [daa]
[bcc] [cbb] [bdd] [dbb] [cdd] [dcc]
[abc] [abd] [acd] [bcd]
Table 3. Cycles needed for 4527 algebras, by atoms
5
6
ROGER D. MADDUX
algorithm for determing whether a finite RA is in RRA, and indeed there is not, as
was proved by Hirsch-Hodkinson [14]. On the other hand, if A ∈ RA ∼ RRA, then
this fact can be detected, either by eventually finding that A has no relational basis
,
of a some finite dimension, or else by checking each of the equations Ern (1n) with
n, r < ω until some equation is found that fails in A (or similarly using any other
recursive equational basis for RRA).
These tests have been carried out on 4527 integral relation algebras, using (J),
(L), and (M), where (with the convention that (xij )˘ = xji )
(J)
x01 ≤ x02 ;x21 · x03 ;x31 ∧ x20 ;x03 · x21 ;x13 ≤ x24 ;x43 ⇒
x01 ≤ (x02 ;x24 · x03 ;x34 );(x42 ;x21 · x43 ;x31 ),
(L)
x02 ;x21 · x03 ;x31 · x04 ;x41 ≤
x02 ; x20 ;x03 · x21 ;x13 · (x20 ;x04 · x21 ;x14 );(x40 ;x03 · x41 ;x13 ) ;x31 ,
(M)
x01 · (x02 · x03 ;x32 );(x21 · x24 ;x41 ) ≤
x03 ; (x30 ;x01 · x32 ;x21 );x14 · x32 ;x24 · x30 ;(x01 ;x14 · x02 ;x24 ) ;x41 .
and checking for the presence of a 5-dimensional relational basis. (J), (L), and (M)
hold in every RA5 . Therefore, if (J), (L), or (M) fails in a finite A ∈ RA then A ∈
RA4 ∼ RA5 . If (J), (L), and (M) all hold in A, then A may still fall into RA4 ∼ RA5
by failing to have a 5-dimensional relational basis. Every 5-dimensional relational
basis has to be included in Bn A ∼ Forbn (A), and this set is a 5-dimensional relational
basis for a simple RA iff it is not empty. We therefore say that Bn A ∼ Forbn (A) is the
maximum n-dimensional relational basis for A. Note that Bn A ∼ Forbn (A)
is empty iff A ∈ RA ∼ RA5 . Another possibility is that B5 A is a 5-dimensional
relational basis. If not, and some 5-dimensional relational basis exists, then we
say the algebra has a proper 5-dimensional relational basis. Table 4 has the
numbers of algebras that fall into ten mutually exclusive categories. The categories
and the labels for them are as follows:
- JLM is the number of RAs in which (J), (L), and (M) all fail.
- JL is the number of RAs in which (J) and (L) fail but (M) holds.
- JM is the number of RAs in which (J) and (M) fail but (L) holds.
- LM is the number of RAs in which (L) and (M) fail but (J) holds.
- J is the number of RAs in which (J) fails but (L) and (M) hold.
- L is the number of RAs in which (L) fails but (J) and (M) hold.
- M is the number of RAs in which (M) fails but (J) and (L) hold.
- N5 is the number of RAs that have no 5-dimensional relational basis, and
in which (J), (L), and (M) hold.
- P5 is the number of RAs that have a proper 5-dimensional relational basis,
- B5 is the number of RAs A in which B5 A is a 5-dimensional relational basis.
The entries in Table 4 may be correlated with those in Table 1. From Table 1
,
we know there are 37 relation algebras with atoms 1 , a, r, and r̆. In Table 4
the line with 37 in the first column tells us that, among these 37 algebras, some
combination of (J), (L), and (M) fails in nine of them. These nine algebras are
therefore not in RA5 (and not representable). There is one more in which (J), (L),
and (M) hold, and yet this algebra is not in RA5 , because it has no 5-dimensional
relational basis. There are two more algebras among these 37 in which B5 A is not
a 5-dimensional relational basis. Each of them does have a proper 5-dimensional
relational basis. Finally, in the remaining 25 algebras, B5 A is a 5-dimensional
FINITE INTEGRAL RELATION ALGEBRAS
total
1
2
3
7
37
65
1316
3013
7
JLM JL JM LM
J L
M N5 P5 B5
0
0
0
0
0 0
0
0
0
1
0
0
0
0
0 0
0
0
0
2
0
0
0
0
0 0
0
0
0
3
0
0
0
0
0 0
0
0
1
6
5
0
2
0
0 0
2
1
2 25
5
2
3
0
0 0
6
3
8 38
369 76 127
16 37 0 132 75 60 424
741 168 495
1 132 2 454 224 188 608
Table 4. Classification of 4527 algebras
relational basis. Among these 37 algebras, 27 are in RA5 and the other 10 are not
in RA5 (and not representable). S. D. Comer has accumulated representations for
many finite relation algebras with up to four atoms; see Comer [6, 4, 5, 7, 8, 9, 10,
11, 12]. Comer found representations for all but five of the 102 algebras 137 , . . . ,
3737 , 165 , . . . , 6565 . One of these five algebras was 2837 , in which (J), (L), and (M)
hold and yet there is no 5-dimensional relational basis. Two others turned out to
be in RA5 ∼ RA6 , namely 3237 and 6065 .
4. Finite integral relation algebras with 0, 1, 2, or 3 atoms
An isomorphism type is a class of algebras of the form I{A} for some algebra
A. There are exactly 18 isomorphism types of finite relation algebras with no more
than three atoms. Thirteen of these types contain only integral algebras. These 13
types account for the first four lines of Table 4. In our survey of these isomorphism
types we continue to follow conventional mathematical practice and refer to algebras
instead of isomorphism types of algebras. We therefore say, for example, that there
are exactly 18 finite relation algebras with no more than three atoms. This leads us
to write “=” in places where it would be more precise to write “∼
=”. The 13 finite
integral relation algebras with 1, 2, or 3 atoms fall into four sets of size 1, 2, 3,
and 7. These algebras have been arranged and numbered so that these four sets of
algebras are {11 }, {12 , 22 }, {13 , 23 , 33 }, and {17 , 27 , 37 , 47 , 57 , 67 , 77 }. For example,
,
57 is the fifth algebra in the list of seven relation algebras whose atoms are 1 , a, b.
As was first observed by Jónsson-Tarski [15, 4.18(ii)], integral relation algebras
are simple, so these 13 algebras are also simple. The other 5 algebras with no more
than three atoms are not integral and also not simple. The smallest non-integral
simple relation algebra is the 4-atom square relation algebra Re (2). Lyndon [17,
p. 307, fn. 13] initiated the enumeration of finite relation algebras, and reported
that every one of the 13 integral relation algebras with no more than three atoms
is commutative and isomorphic to a subalgebra of the complex algebra of either
a cyclic group of order not exceeding 13 or the group of rational numbers under
addition. (See also McKenzie [20, p. 286, §5, P1].) Explicit representations for
some small simple relation algebras are given in R. McKenzie’s dissertation [19,
pp. 38–40], and in F. Backer’s seminar report [2, pp. 11–20]. A simple 8-element
relation algebra was missed in the latter survey, and an 8-element direct product
of two simple relation algebras was omitted from the former. Backer [2] contains
8
ROGER D. MADDUX
,
11 1
,
,
1 1
Table 5. Cycle and table for the algebra 11 = M1 = N11
11
, , ,
111
a representation on infinitely many elements for the relation algebra 77 , but a
representation of 77 on 9 elements was found by Ulf Wostner around 1976.
The spectrum of a relation algebra A ∈ RA is the set of cardinalities of sets on
which there is a simple representation of A:
spec(A) = {k : A ∼
= | ⊆ Re (U ) , |U | = k}.
For example, the spectrum of the trivial (1-element) algebra Re (0) is {0}, the
spectrum of Re (n) is {n} for every n ∈ ω, the spectrum of any nonrepresentable
relation algebra is ∅, and the spectrum of a nontrivial direct product of finite relation
algebras is also ∅. The spectra of the algebras 11 , 12 , 22 , 13 , 23 , 33 , 17 , 27 , 37 , 47 ,
57 , 67 , and 77 were determined in Andréka-Maddux [1].
We say ρ is a square representation of A ∈ RA on U ∈ V if ρ is an embedding
of A into Re (U ). We say that a square representation ρ of A on U is unique if
there is no other square representation of A on a set of cardinality |U |, that is, if σ
is a square representation of A on V ∈ V and |U | = |V |, then there is a bijection
f : U → V such that σ(x) = f −1 |ρ(x)|f for every x ∈ A. We say that a square
representation ρ of A on U is minimal if there is no square representation of A on
a smaller set, that is, if σ is a square representation of A on V ∈ V then |U | ≤ |V |.
It is shown in Andréka-Maddux [1] that the minimal representation is unique for
each of the 13 integral algebras 11 , 12 , 22 , 13 , 23 , 33 , 17 , 27 , 37 , 47 , 57 , 67 , 77 .
Each of the 18 relation algebras with three or fewer atoms is examined below.
The first four algebras are the subalgebras of Re (0), Re (1), Re (2), and Re (3)
generated by ∅. After these first four algebras this sequence is constant.
4.1. The trivial algebra. The universe of Re (0) is {∅}, so Re (0) is the trivial
algebra has exactly one element. Re (0) is generated by ∅. In Re (0), we have
,
,
0 = 1 = 0 = 1. The spectrum of Re (0) is {0}. There is no multiplication table
for the atoms of Re (0) because Re (0) has no atoms and no cycles.
4.2. The 1-atom algebra. There is exactly one relation algebra with one atom,
,
,
called 11 . There are exactly two elements in the algebra 11 , and 0 = 0 < 1 = 1.
,
, , ,
The only atom of 11 is 1 , and 11 has a single cycle, namely [1 , 1 , 1 ]. This cycle
and the multiplication table for the atom of 11 are shown in Table 5. The algebra
11 is generated by ∅, is the complex algebra of the 1-element group, has a unique
minimal square representation on a 1-element set.
11 = Sg(Re(1)) ∅ = Re (1) = Cm (Z1 ),
spec(11 ) = {1}.
4.3. The algebras 12 and 22 . There are just two relation algebras with exactly
,
two atoms, 11 and 12 . Both of these algebras have four elements, namely 0, 1 ,
,
,
,
, , ,
0 , and 1. Their atoms are 1 and 0 . The algebra 12 has two cycles, [1 , 1 , 1 ]
, , ,
, , ,
, , ,
and [1 , 0 , 0 ], and one forbidden cycle, [0 , 0 , 0 ]. The cycles of 22 are [1 , 1 , 1 ],
, , ,
, , ,
[1 , 0 , 0 ], and [0 , 0 , 0 ]. The cycles and multiplication tables for the atoms of
11 and 12 are shown in Table 6. The + signs are omitted in the multiplication
FINITE INTEGRAL RELATION ALGEBRAS
12
,
1
,
0
Table 6. Cycles and tables for
, , ,
111
, , ,
111
12
22
u
, , ,
100
, , ,
100
a
···
, , ,
000
,
,
,
,
1 0
22 1
0
,
,
,
,
,
1 0
1 1
0
, ,
,
, , ,
0 1
0 0 10
12 = M2 and 22 = M3
u
u
9
a
u
a
u
a
Figure 1. Square representations of 12 = M2 and 22 = M3
2
(11 )
(12 )2
e0 e0 e0
e0 e0 e0
e1 e1 e1
e1 e1 e1
···
e2 e2 e2
(11 )2
e0
e1
e0
e0
0
e1
0
e1
(12 )3
e0
e1
e2
e0
e0
0
0
e1
0
e1
0
e2
0
0
e2
Table 7. Cycles and tables for algebras (11 )2 and (12 )3
tables for atoms to save space. For example, from the table for 22 we find that
, ,
, ,
,
,
0 ;0 = 1 0 = 1 + 0 = 1. The algebra 12 is the proper subalgebra of Re (2)
generated by ∅, is the complex algebra of the 2-element group Z2 , and has a square
representation on a 2-element set that is minimal and unique.
12 = Sg(Re(2)) (∅) = Cm (Z2 ),
spec(12 ) = {2}.
The square representation ρ of 12 on 2, determined by
,
,
ρ (1 ) = {h0, 0i , h1, 1i},
ρ (0 ) = {h0, 1i , h1, 0i},
is shown in Figure 1, where 0 and 1 are represented by black spots. The identity
relation is not explicitly shown (but could be illustrated by loops connecting each
,
spot to itself), and the two ordered pairs h0, 1i and h1, 0i in ρ (0 ) are indicated
jointly by a single line connecting the two spots. On the other hand, the algebra
22 has an infinite spectrum,
spec(22 ) = {k : 3 ≤ k},
because, for every cardinal k ≥ 3, there is a unique square representation ρ that
,
,
embeds 22 into Re (k), where ρ (1 ) = k 1 and ρ (0 ) = k 2 ∼ k 1 . This representation
is shown in Figure 1 for the case k = 3. This same map embeds 22 into Cm (Zk ).
Whenever k ≥ 3, 22 is the proper subalgebra of Re (k) generated by ∅.
22 = Sg(Re(k)) (∅) ⊂ Re (k) ,
22 ∈ SCm (Zk ).
4.4. The algebras (11 )2 and (11 )3 . These are the first two of four algebras that
are direct products of some of those already examined. Note that A × Re (0) ∼
=A
so we do not consider products in which one of the factors is Re (0).
All the atoms of (11 )2 are identity atoms, and there are exactly two of them,
say e0 and e1 . The cycles of (11 )2 , which are [e0 , e0 , e0 ] and [e1 , e1 , e1 ], and the
multiplication table for atoms of (11 )2 are shown in Table 7. (11 )2 is a Boolean
relation algebra, and (11 )2 is isomorphic to the Boolean relation algebra obtained
from any finite Boolean algebra with exactly two atoms. (11 )2 is isomorphic to
10
ROGER D. MADDUX
11 × 12
11 × 22
e0 e0 e0
e0 e0 e0
e1 e1 e1
e1 e1 e1
, ,
e1 0 0
, ,
e1 0 0
···
, , ,
000
,
,
11 × 12 e0 e1 0
11 × 22 e0 e1
0
e0 e0 0 0
e0 e0 0
0
,
,
e1 0 e1 0
e1 0 e1
0
,
,
,
,
,
0 0 0 e1
0 0 0 e1 0
Table 8. Cycles and tables for algebras 11 × 12 and 11 × 22
Sb (E) whenever E is an equivalence relation with exactly two equivalence classes,
each of which contains exactly one element.
The algebra (11 )3 has three atoms, and all of them are identity atoms, say e0 , e1 ,
and e2 . The cycles of 11 are [e0 , e0 , e0 ], [e1 , e1 , e1 ], and [e2 , e2 , e2 ]. The cycles and the
multiplication table for atoms is shown in Table 7. The algebra 11 is isomorphic to
the Boolean relation algebra obtained from any finite Boolean algebra with exactly
three atoms, and 11 is isomorphic to Sb (E) whenever E is an equivalence relation
with exactly three equivalence classes, each of which contains exactly one element.
The algebras 11 , (11 )2 , and (11 )3 are the first three in the infinite sequence of
algebras (Re (1))n with 1 ≤ n < ω,
11 ∼
= Re (1) , (11 )2 ∼
= (Re (1))2 , (11 )3 ∼
= (Re (1))3 , · · ·
For 1 ≤ n < ω, (Re (1))n is a finite Boolean relation algebra with n atoms, which
is isomorphic to Sb (E) iff E is an equivalence relation with exactly n equivalence
classes containing one element each.
4.5. The algebras 11 × 12 and 11 × 22 . Both of these algebras have three atoms.
,
Two of them are identity atoms, say e0 and e1 , and 0 is the sole diversity atom.
, ,
The cycles of 11 ×12 are [e0 , e0 , e0 ], [e1 , e1 , e1 ], and [e1 , 0 , 0 ]. There is one forbidden
, , ,
, ,
diversity cycle, [0 , 0 , 0 ]. The cycles of 11 × 22 are [e0 , e0 , e0 ], [e1 , e1 , e1 ], [e1 , 0 , 0 ],
, , ,
and [0 , 0 , 0 ]. There are no forbidden cycles. The cycles and multiplication tables
for the atoms of 11 ×12 and 11 ×22 are shown in Table 8. We obtain representations
for these algebras by combining representations for their factors. Consider the
equivalence relation E in Re (3) whose equivalence classes are {0} and {1, 2}, that
is, E = {h0, 0i , h1, 1i , h2, 2i , h1, 2i , h2, 1i} ⊆ 32 . For a representation of 11 × 12 over
E, set
ρ (e0 ) = {h0, 0i},
ρ (e1 ) = {h1, 1i , h2, 2i},
,
ρ (0 ) = {h1, 2i , h2, 1i}.
Consider the equivalence relation E in Re (k + 1) with 3 ≤ k where E = {h0, 0i} ∪
{1, . . . , k}2 ⊆ (k + 1)2 . For a representation ρ of 11 × 22 over E, set
ρ (e0 ) = {h0, 0i},
ρ (e1 ) = {h1, 1i , . . . , hk, ki},
,
ρ (0 ) = {1, 2, 3}2 ∼{1, . . . , k}1 .
Finally, we note that
11 × 12 ∼
= Re (1) × Sg(Re(2)) (∅)
and, for all k ≥ 3,
11 × 22 ∼
= Re (1) × Sg(Re(k)) (∅).
FINITE INTEGRAL RELATION ALGEBRAS
13
23
33
13
,
1
r
r̆
, , ,
111
, , ,
111
, , ,
111
, , ,
111
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
1 rr
,
1 rr
,
1 rr
,
1 rr
rrr
rrr
···
rrr
,
,
1
r
r̆
23 1 r r̆
,
,
,
1
r
r̆
1 1 r r̆
,
,
r
r
1 rr̆
r r r̆ 1
,
,
r̆ 1 rr̆
r̆
r̆ r̆ 1 r
Table 10. Cycles and tables for
11
rrr̆
···
rrr̆
rrr̆
,
33 1
,
,
1 1
r r
r̆ r̆
algebras
r
r̆
r
r̆
,
rr̆ 1 rr̆
,
1 rr̆ rr̆
13 –33
4.6. The algebra 13 . This is the first of three algebras, 13 –33 , that are integral
,
,
and have the atoms 1 , r, and r̆. The only symmetric atom is 1 . The other two
atoms, r and r̆, are converses of each other. The identity cycles of the algebras
, , ,
,
,
13 –33 are [1 , 1 , 1 ], [1 , r, r], and [r, 1 , r].
These algebras are distinguished by their choice of diversity cycles from these
options: [r, r, r] and [r, r, r̆]. All three nonempty combinations of the diversity cycles
produce representable relation algebras. The algebras and their cycles are shown
in Table 10. Algebra 13 is a subalgebra of Re (Q), where Q is the set of rational
numbers. In fact, 13 ∼
= Sg(Re(Q)) {<}, where < is the natural linear ordering of
Q. Conversely, if ρ is a square representation of 13 , then ρ (r) and ρ (r̆) are dense
linear orderings without endpoints. We therefore have
spec(13 ) = {k : ω ≤ k}
because there is a dense linear ordering without endpoints on every infinite set and
on no finite set.
Algebra 13 is the only one among the 18 relation algebras with no more than
three atoms that has no square representation over a finite set. In general, if A is a
finite integral relation algebra with an asymmetric atom r such that r ;r = r, then
r must be assigned by any representation of A to a dense linear ordering without
endpoints. Examples of finite integral representable relation algebras that have no
square representations on finite set for this reason are 137 , 237 , 737 , 837 , 1337 , and
1537 . A symmetric representable relation algebra which also has no representation
on a finite set, but for a different reason, is 2465 .
4.7. The algebra 23 . The algebra 23 is a subalgebra of Re (3). Let +n be addition
modulo n, where 1 ≤ n < ω, i.e., for all i, j ∈ n,
(
i+j
i +n j =
i+j−n
if i + j < n
.
if n ≤ i + j < 2n
12
ROGER D. MADDUX
u
J r
r J
J
^
J
u
u
r
Figure 2. Unique square representation of 23
We may use this operation to describe groups and representations. For example,
the cyclic group of order 3 is Z3 = h3, +3 i. If
,
ρ (1 ) = {hi, i +3 0i : i ∈ 3} = {h0, 0i , h1, 1i , h2, 2i},
ρ (r) = {hi, i +3 1i : i ∈ 3} = {h0, 1i , h1, 2i , h2, 0i},
ρ (r̆) = {hi, i +3 2i : i ∈ 3} = {h0, 2i , h1, 0i , h2, 1i},
then ρ extends to an embedding of 23 into Re (3) and Cm (Z3 ). In fact, we have
23 ∼
= Sg(Re(3)) {ρ (r)} ⊆ Re (3) ,
and the multiplication table for the atoms of 23 is the same as the multiplication
table for Z3 . Thus 23 is the complex algebra of the cyclic group of order 3 and has
a small spectrum:
13 ∼
spec(23 ) = {3}.
= Cm (Z3 ),
The unique minimal square representation ρ of 23 is portrayed in Figure 2, in which
the arrows represent the relation assigned to the atom r.
4.8. The algebra 33 . We have 33 ∼
= Sg(Re(7)) {ρ (r)}, where ρ is the representation
defined on the atoms by
,
ρ (1 ) = {hi, ii : i ∈ 7},
ρ (r) = {hi, i +7 ji : i ∈ 7, j ∈ {1, 2, 4}},
ρ (r̆) = {hi, i +7 ji : i ∈ 7, j ∈ {3, 5, 6}}.
This representation is the unique minimal square representation of 33 on a 7-element
set. It also embeds 33 into Cm (Z7 ), so
33 ∈ SCm (Z7 ).
It is a peculiar combinatorial fact that 33 has an isolated gap in its spectrum.
Indeed,
spec(33 ) = {7} ∪ {k : 9 ≤ k}.
For a proof, see Andréka-Maddux [1, Th. 4.2]. It would be interesting to know
whether other finite relation algebras exhibit this character.
4.9. The algebras 17 –77 . The seven algebras 17 –77 are integral and have three
,
symmetric atoms. One of the atoms is 1 , and the other two are a and b. The
, , ,
,
,
identity cycles [1 , 1 , 1 ], [1 , a, a], and [1 , b, b] appear in all seven algebras. The
diversity cycles are [a, a, b], [a, b, b], [b, b, b], and [a, a, a]. Every combination of
diversity cycles produces a representable relation algebra. Up to isomorphism,
there are just seven different choices. The cycles and tables for the algebras 17 –77
are shown in Table 12.
4.10. The algebra 17 . To obtain a representation of 17 , let
,
ρ (1 ) = {hi, ii : i ∈ 4},
ρ (a) = {hi, i +4 2i : i ∈ 4},
ρ (b) = {hi, i +4 ji : i ∈ 4, j ∈ {1, 3}}.
Then ρ extends to a unique minimal square representation of 17 on 4 = {0, 1, 2, 3}
and
17 ∼
= Sg(Re(4)) {ρ (a)} = Sg(Re(4)) {ρ (b)}.
FINITE INTEGRAL RELATION ALGEBRAS
17
27
37
47
57
67
77
17
,
1
a
b
,
1
,
1
a
b
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
a
b
27
,
a
b
1
,
1
b
a
,
b 1a
b
,
57 1
a
,
,
1 1
a
,
a a 1b
b b ab
Table
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 bb
,
1 bb
,
1 bb
,
1 bb
,
1 bb
,
1 bb
,
1 bb
,
1 bb
aaa bbb abb
· · · · · · abb
aaa · · · abb
· · · bbb abb
aaa bbb abb
· · · · · · abb
aaa · · · abb
aaa bbb abb
13
baa
···
···
···
···
baa
baa
baa
,
,
,
1
a
b
37 1 a
b
47 1
a
b
,
,
,
,
,
1
a
b
1 1 a
b
1 1
a
b
,
,
,
a 1a b
a a 1
b
a a 1a
b
,
,
,
b
b 1a
b b b 1 ab
b b
b 1 ab
,
,
77 1
a
b
67 1
a
b
b
,
,
,
,
1 1
a
b
1 1
a
b
b
,
,
a a 1 ab ab
a a 1 ab ab
ab
,
,
,
b b
ab 1 ab
b b
ab 1 a
1a
12. Cycles and tables for algebras 17 –77
u
a
b
u
u
b
b
a
u
Figure 3. Unique minimal square representation of 17
In Figure 3, ρ(a) is the set of pairs connected by solid lines and ρ(b) is the set of
pairs connected by dashed lines. Thus 17 is a subalgebra of Re (4), and the same
map shows that
17 ∈ SCm (Z4 ).
The algebra 17 is also a subalgebra of complex algebra of the 4-element group Z22
via the map σ that sends a to “add h1, 0i” and b to “add h0, 1i or h1, 1i”. In more
detail, if
,
σ (1 ) = {hhi, ji , hi, jii : i, j ∈ 2},
σ (a) = {hhi, ji , hi +2 1, jii : i, j ∈ 2},
σ (b) = {hhi, ji , hi, j +2 1ii : i, j ∈ 2} ∪ {hhi, ji , hi +2 1, j +2 1ii : i, j ∈ 2},
then σ extends to an embedding of 17 into Cm Z22 , hence
17 ∈ SCm Z22 .
Figure 3 is also an illustration of σ if the dots are properly identified with the
elements of Z22 . The algebra 17 has a small spectrum:
spec(17 ) = {4}.
14
ROGER D. MADDUX
u
u
u
u
u
u
Figure 4. Unique minimal square representation of 27
4.11. The algebra 27 . Suppose ρ is a square representation of 27 that embeds
,
27 into Re (U ). Let E = ρ (1 + a). Inspection of the multiplication table for 27
reveals that E is an equivalence relation with exactly two equivalence classes, each
of which contains at least three elements. Hence |U | ≥ 6. Conversely, if E is such
an equivalence relation on a set U , then 27 can be embedded into Re (U ) by the
,
map that takes 1 + a to E and b to U 2 ∼ E. Thus we have
spec(27 ) = {k : 6 ≤ k}.
For an equivalence relation having two equivalence classes of three elements each,
the representation is minimal and unique. This representation is shown in Figure 4.
Furthermore,
27 ∈ SCm (Z2 × Z3 ),
for if we let
,
ρ (1 ) = {hhi, ji , hi, jii : i ∈ 2, j ∈ 3},
ρ (a) = {hhi, ji , hi, j +3 kii : i ∈ 2, j ∈ 3, k ∈ {1, 2}},
ρ (b) = {hhi, ji , hi +2 1, kii : i ∈ 2, j, k ∈ 3},
then ρ extends to an embedding of 27 into Cm (Z2 × Z3 ), and
27 ∼
= Sg(Cm(Z2 ×Z3 )) {ρ (a)} = Sg(Cm(Z2 ×Z3 )) {ρ (b)}.
4.12. The algebra 37 . Suppose ρ is an embedding of 37 into Re (U ). Then ρ (a)
,
,
must be a transposition because a;a = 1 . Let E = ρ (1 + a). Further inspection
of the table shows that E is an equivalence relation with three or more equivalence
classes, each of which contains exactly two elements. Thus |U | ≥ 6. Conversely,
if E is such an equivalence relation on U , then 37 can be embedded in Re (U ) by
,
the map that sends 1 + a to E and b to U 2 ∼ E. If E is an equivalence relation
having exactly three equivalence classes of two elements each, the representation is
minimal and unique. This representation is shown in in Figure 5. Thus we have
spec(37 ) = {2k : 3 ≤ k}.
Furthermore,
37 ∈ SCm (Z2 × Z3 ),
FINITE INTEGRAL RELATION ALGEBRAS
u
u
u
u
u
u
15
Figure 5. Unique minimal square representation of 37
u
u
u
u
u
u
u
u
u
Figure 6. Unique minimal square representation of 47
for if we let
,
ρ (1 ) = {hhi, ji , hi, jii : i ∈ 2, j ∈ 3},
ρ (a) = {hhi, ji , hi +2 1, jii : i ∈ 2, j ∈ 3},
ρ (b) = {hhi, ji , hk, j +3 lii : i, k ∈ 2, j ∈ 3, l ∈ {1, 2}},
then ρ extends to an embedding of 37 into Cm (Z2 × Z3 ), and
37 ∼
= Sg(Cm(Z2 ×Z3 )) {ρ (a)} = Sg(Cm(Z2 ×Z3 )) {ρ (b)}.
4.13. The algebra 47 . Suppose ρ is a square representation of 47 that embeds
,
47 into Re (U ). Let E = ρ (1 + a). Then E is an equivalence relation on U with
three or more equivalence classes (because b ≤ b;b), each of which has at least three
elements (because a ≤ a;a). Any such equivalence relation gives rise to a square
representation of 47 , so we have
spec(47 ) = {k : 9 ≤ k}.
If E has exactly three equivalence classes with exactly three elements each, the
resulting square representation
is minimal and unique. It is shown in Figure 6. We
can embed 47 into Cm Z23 via ρ if we set
,
ρ (1 ) = {hhi, ji , hi, jii : i ∈ 3, j ∈ 3},
ρ (a) = {hhi, ji , hi +3 k, jii : i, j ∈ 3, k ∈ {1, 2}},
ρ (b) = {hhi, ji , hk, j +3 lii : i, k ∈ 3, j ∈ 3, l ∈ {1, 2}},
then ρ extends to an embedding which shows
2
2
47 ∈ SCm Z23 , 47 ∼
= Sg(Cm(Z3 )) {ρ (a)} = Sg(Cm(Z3 )) {ρ (b)}.
16
ROGER D. MADDUX
u
b
u
u
a
u
u
Figure 7. Unique square representation of 57
We can also embed 47 into Cm (Z9 ) via σ if we set
,
σ (1 ) = {hi, ii : i ∈ 9},
σ (a) = {hi, i +3 ji : i ∈ 3, j ∈ {3, 6}},
σ (b) = {hi, i +3 ji : i ∈ 3, j ∈ {2, 4, 5, 7, 8}},
obtaining
47 ∼
= Sg(Cm(Z9 )) {σ (a)} = Sg(Cm(Z9 )) {σ (b)}.
These embeddings of 47 into Cm Z23 and Cm (Z9 ) can be seen in Figure 6 if the
spots are properly identified with elements of Z23 and Z9 .
47 ∈ SCm (Z9 ),
4.14. The algebra 57 . It is an interesting exercise to show that if ρ is a square
representation of 57 that embeds 57 into Re (U ), then |U | = 5 and ρ must be the
representation pictured in Figure 7. Thus we have
spec(57 ) = {5}.
Figure 7 shows ρ (a) as a pentagon and ρ (b) as a pentagram, so 57 has been called
the pentagonal relation algebra. For an embedding of 57 into Cm (Z5 ), let
,
ρ (1 ) = {hi, ii : i ∈ 5},
ρ (a) = {hi, i +5 ji : i ∈ 5, j ∈ {1, 4}},
ρ (b) = {hi, i +5 ji : i ∈ 5, j ∈ {2, 3}}.
It happens that if A ∈ RA, A is atomic and integral, and |AtA| ≤ 3, then B5 A is a
5-dimensional relational basis for A, unless A = 57 . For a finite A ∈ RA let us say
that two 4-by-4 basic matrices a, b ∈ B4 A are permutation-equivalent if there is
a permutation π : 4 → 4 such that b = aπ. Furthermore, a ∈ B4 A is a forbidden
minor of A if a cannot be obtained from any 5-by-5 matrix in the maximum 5dimensional relational basis of A by selecting an entry on the main diagonal and
deleting the row and column that contain that entry. If a basic matrix is forbidden,
then so are all basic matrices that are permutation-equivalent to it. Therefore, if
a finite integral relation algebra A has a proper maximum 5-dimensional relational
basis, then that basis may be succinctly described just by listing a forbidden minor
from each of the permutation-equivalence classes of forbidden minors. The basis
then consists of all those matrices in B5 A that do not contain one of the listed
minors. The forbidden minors of each algebra can be completely specified by giving
FINITE INTEGRAL RELATION ALGEBRAS
17
u
u
u
u
u
u
u
u
Figure 8. A square representation of 67
only the entries above the main diagonal. For example, the forbidden minors of
algebra 57 are
[a01 , a02 , b03 , b12 , a13 , a23 ],
[a01 , b02 , b03 , b12 , b13 , a23 ]
which is a short-hand for the following two matrices:
 ,

 ,
1 a a b
1 a b
 a 1, b a 
 a 1, b



 a b 1, a 
 b b 1,
,
b a a 1
b b a

b
b

a
,
1
Notice that neither of these two matrices can be found in the representation in
Figure 7 (no four spots are related to each other in the way described by the
matrices). On the other hand, both of these matrices belong to B4 A, which is a
4-dimensional relational basis for 57 , as it is for all finite relation algebras.
4.15. The algebra 67 . Andréka-Maddux [1, Th. 7] proved
spec(67 ) = {k : 8 ≤ k}.
A unique minimal representation of 67 in Re (8) is shown in Figure 8, which also
illustrates the fact that we obtain
67 ∈ SCm (Z8 )
via ρ if we set
,
ρ (1 ) = {hi, ii : i ∈ 8},
ρ (a) = {hi, i +8 ji : i ∈ 8, j ∈ {2, 3, 5, 6}},
ρ (b) = {hi, i +8 ji : i ∈ 8, j ∈ {1, 4, 7}}.
4.16. The algebra 77 . Andréka-Maddux [1, Th. 8] proved
spec(77 ) = {k : 9 ≤ k}.
A unique minimal representation of 67 in Re (9) is shown in Figure 9. This representation was found by Ulf Wostner around 1976. It also shows that we can embed
18
ROGER D. MADDUX
u
u
u
u
u
u
u
u
u
Figure 9. A square representation of 77
77 into Cm Z23 by setting
,
ρ (1 ) = {hhi, ji , hi, jii : i ∈ 3, j ∈ 3},
ρ (a) = {hhi, ji , hi +3 k, jii : i, j ∈ 3, k ∈ {1, 2}}
∪ {hhi, ji , hi, j +3 kii : i, j ∈ 3, k ∈ {1, 2}},
,
ρ (b) = 92 ∼ ρ (a) ∼ ρ (1 ) .
By the way, in Figure 9, the graph of the solid lines is isomorphic to the graph of
the dashed lines.
5. Finite integral relation algebras with 4 or 5 atoms
From Table 3 we see that there are 37 isomorphisms types of integral relation
,
algebras whose atoms are 1 , a, r, and r̆. The identity cycles for all of these algebras
, , , ,
,
,
are [1 , 1 , 1 ], 1 , a, a], [r, 1 , r], and [1 , r, r]. The potential diversity cycles are
[a, a, a], [r, r, r], [r, r, r̆], [a, r, r], [r, a, r], r, a, a], [r, r, a].
Any selection of diversity cycles from this list produces an NA. There are 27 = 128
such choices. The ordering of the diversity cycles in this list (which is the same as in
Table 2) determines an linear ordering on the resulting NAs via reverse lexicographic
ordering of the cycles. For example, choosing none of the diversity cycles gives the
first NA, and choosing all of them gives the last one. Suppose that A ∈ NA is the
result of choosing some of these diversity cycles, and that the first cycle, [a, a, a],
is not a cycle of A. Adding this cycle to the cycles of A will produce the next NA.
In the list of 37 relation algebras below, a choice of diversity cycles appears if it
meets two criteria. First, the choice must produce a relation algebra A. Second, no
earlier choice produces an algebra isomorphic to A. The remaining lists of cycles
thus determine 37 relation algebras that are not isomorphic to each other. These
algebras are then numbered from 137 to 3737 . This same plan has been used on the
lists of cycles in Table 2 to give names to the 4527 integral relation algebras with
five or fewer atoms.
6. Cycles of the algebras 137 –3737
137
, , ,
111
, , ,
111
,
,
1 aa r1 r
,
,
1 aa r1 r
,
1 rr
,
1 rr
aaa rrr
· · · rrr
rrr̆
···
arr
arr
rar
rar
raa
···
rra
···
FINITE INTEGRAL RELATION ALGEBRAS
237
337
437
537
637
737
837
937
1037
1137
1237
1337
1437
1537
1637
1737
1837
1937
2037
2137
2237
2337
2437
2537
2637
2737
2837
2937
3037
3137
3237
3337
3437
3537
3637
3737
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
, , ,
111
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
1 aa
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
r1 r
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
,
1 rr
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
···
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr
rrr
···
···
rrr
rrr
rrr̆
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
···
rrr̆
···
···
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
arr
arr
arr
arr
arr
···
···
arr
arr
arr
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
19
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
rar
rar
rar
rar
···
···
rar
rar
rar
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
raa
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
7. Multiplication tables for algebras 137 –3737
137
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
a
,
1
r
r̆
r
r
r
r
,
1 arr̆
r̆
r̆
r̆
,
1 arr̆
r̆
237
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
r
a
r
,
1a
r
r
r
,
r̆ 1 arr̆
r̆
r̆
r̆
,
1 arr̆
r̆
rra
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
20
ROGER D. MADDUX
337
,
1
a
r
r̆
537
,
1
a
r
r̆
737
,
1
a
r
r̆
937
,
1
a
r
r̆
1137
,
1
a
r
r̆
1337
,
1
a
r
r̆
1537
,
1
a
r
r̆
1737
,
1
a
r
r̆
1937
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
r
r̆
a
r
r̆
,
1
r
r̆
,
r
r̆ 1 a
,
r̆ 1 a r
a
r
r̆
a
r
r̆
,
1
r
r̆
,
r
rr̆
1 arr̆
,
r̆ 1 arr̆
rr̆
a
r
r̆
a
r
r̆
,
1 rr̆
a
a
,
a
r
1 rr̆
,
a
1 rr̆
r̆
a
r r̆
a
r r̆
,
1 rr̆ a a
,
a
r̆ 1
,
a
1 r
a
r
r̆
a
r
r̆
,
1 rr̆
a
a
,
a
rr̆ 1 rr̆
,
a
1 rr̆ rr̆
a
r
r̆
a
r
r̆
,
1 arr̆ ar
a
,
a
r
1 arr̆
,
ar̆
1 rr̆
r̆
a
r
r̆
a
r
r̆
,
1 arr̆
ar
ar̆
,
ar
r
1 arr̆
,
ar̆
1 arr̆
r̆
a
r
r̆
a
r
r̆
,
1 arr̆
ar
ar̆
,
ar
rr̆
1 arr̆
,
ar̆
1 arr̆
rr̆
a
r
r̆
a
r
r̆
,
1
r̆
r
,
r̆ arr̆ 1 rr̆
,
r 1 rr̆ arr̆
437
,
1
a
r
r̆
637
,
1
a
r
r̆
837
,
1
a
r
r̆
1037
,
1
a
r
r̆
1237
,
1
a
r
r̆
1437
,
1
a
r
r̆
1637
,
1
a
r
r̆
1837
,
1
a
r
r̆
2037
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
r
r̆
a
r
r̆
,
1a r
r̆
,
r
r̆ 1 a
,
r̆ 1 a r
a
r
r̆
a
r
r̆
,
1a
r
r̆
,
r
rr̆
1 arr̆
,
r̆ 1 arr̆
rr̆
a
r
r̆
a
r
r̆
,
1 arr̆
a
a
,
a
r
1 rr̆
,
a
1 rr̆
r̆
a
r r̆
a
r r̆
,
1 arr̆ a a
,
a
r̆ 1
,
a
1 r
a
r
r̆
a
r
r̆
,
1 arr̆
a
a
,
a
rr̆ 1 rr̆
,
a
1 rr̆ rr̆
a
r
r̆
a
r
r̆
,
1 rr̆
ar
ar̆
,
ar
r
1 arr̆
,
ar̆ 1 arr̆
r̆
a
r
r̆
a
r
r̆
,
1 rr̆
ar
ar̆
,
ar
rr̆
1 arr̆
,
ar̆ 1 arr̆
rr̆
a r r̆
a r r̆
,
1 r̆ r
,
r̆ a 1
,
r 1 a
a
r
r̆
a
r
r̆
,
1 a rr̆ rr̆
,
rr̆
a 1a
,
rr̆ 1 a a
FINITE INTEGRAL RELATION ALGEBRAS
2137
,
1
a
r
r̆
2337
,
1
a
r
r̆
2537
,
1
a
r
r̆
2737
,
1
a
r
r̆
2937
,
1
a
r
r̆
3137
,
1
a
r
r̆
3337
,
1
a
r
r̆
3537
,
1
a
r
r̆
3737
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
r
r̆
a
r
r̆
,
1a
rr̆
rr̆
,
rr̆
ar
1 arr̆
,
rr̆ 1 arr̆
ar̆
a
r
r̆
a
r
r̆
,
1 rr̆ ar̆
ar
,
ar̆
ar 1 rr̆
,
ar 1 rr̆ ar̆
a
r
r̆
a
r
r̆
,
1 rr̆ ar̆
ar
,
ar̆
arr̆ 1 rr̆
,
ar 1 rr̆ arr̆
a
r
r̆
a
r
r̆
,
1 rr̆ arr̆
ar
,
ar̆
ar 1 arr̆
,
arr̆ 1 rr̆
ar̆
a
r
r̆
a
r
r̆
,
1 rr̆ arr̆
ar
,
ar̆
arr̆ 1 arr̆
,
arr̆ 1 rr̆ arr̆
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆ arr̆
,
arr̆
a
1a
,
arr̆
1a
a
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆
arr̆
,
arr̆
ar
1 arr̆
,
arr̆ 1 arr̆
ar̆
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆ arr̆
,
arr̆
ar̆ 1 a
,
arr̆
1 a ar
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆
arr̆
,
arr̆
arr̆ 1 arr̆
,
arr̆ 1 arr̆ arr̆
2237
,
1
a
r
r̆
2437
,
1
a
r
r̆
2637
,
1
a
r
r̆
2837
,
1
a
r
r̆
3037
,
1
a
r
r̆
3237
,
1
a
r
r̆
3437
,
1
a
r
r̆
3637
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
,
1
,
1
a
r
r̆
a
r
r̆
a
r
r̆
,
1a
rr̆
rr̆
,
rr̆
arr̆ 1 arr̆
,
rr̆ 1 arr̆ arr̆
a
r
r̆
a
r
r̆
,
1 arr̆ ar̆
ar
,
ar̆
ar 1 rr̆
,
ar
1 rr̆ ar̆
a
r
r̆
a
r
r̆
,
1 arr̆ ar̆
ar
,
ar̆
arr̆ 1 rr̆
,
ar
1 rr̆ arr̆
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆
ar
,
ar̆
ar 1 arr̆
,
arr̆ 1 rr̆
ar̆
a
r
r̆
a
r
r̆
,
1 arr̆ arr̆
ar
,
ar̆
arr̆ 1 arr̆
,
arr̆ 1 rr̆ arr̆
a
r
r̆
a
r
r̆
,
1 rr̆ arr̆
arr̆
,
arr̆
ar
1 arr̆
,
arr̆ 1 arr̆
ar̆
a
r
r̆
a
r
r̆
,
1 rr̆ arr̆ arr̆
,
arr̆ ar̆ 1 a
,
arr̆ 1 a ar
a
r
r̆
a
r
r̆
,
1 rr̆ arr̆
arr̆
,
arr̆
arr̆ 1 arr̆
,
arr̆ 1 arr̆ arr̆
8. Diversity cycles for the algebras 165 –6565
21
22
ROGER D. MADDUX
165
265
365
465
565
665
765
865
965
1065
1165
1265
1365
1465
1565
1665
1765
1865
1965
2065
2165
2265
2365
2465
2565
2665
2765
2865
2965
3065
3165
3265
3365
3465
3565
3665
3765
3865
3965
4065
4165
4265
4365
4465
4565
4665
4765
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
bbb ccc abb baa acc caa bcc cbb abc
· · · · · · abb · · · acc · · · bcc · · · · · ·
· · · · · · abb · · · acc · · · bcc · · · · · ·
bbb · · · abb · · · acc · · · bcc · · · · · ·
bbb · · · abb · · · acc · · · bcc · · · · · ·
· · · ccc abb · · · acc · · · bcc · · · · · ·
· · · ccc abb · · · acc · · · bcc · · · · · ·
bbb ccc abb · · · acc · · · bcc · · · · · ·
bbb ccc abb · · · acc · · · bcc · · · · · ·
· · · · · · abb baa acc · · · bcc · · · · · ·
· · · · · · abb baa acc · · · bcc · · · · · ·
bbb · · · abb baa acc · · · bcc · · · · · ·
· · · ccc abb baa acc · · · bcc · · · · · ·
· · · ccc abb baa acc · · · bcc · · · · · ·
bbb ccc abb baa acc · · · bcc · · · · · ·
· · · · · · · · · baa acc caa bcc · · · · · ·
· · · · · · · · · baa acc caa bcc · · · · · ·
bbb · · · · · · baa acc caa bcc · · · · · ·
bbb · · · · · · baa acc caa bcc · · · · · ·
· · · ccc · · · baa acc caa bcc · · · · · ·
bbb ccc · · · baa acc caa bcc · · · · · ·
· · · · · · abb baa acc caa bcc cbb · · ·
· · · · · · abb baa acc caa bcc cbb · · ·
bbb · · · abb baa acc caa bcc cbb · · ·
bbb ccc abb baa acc caa bcc cbb · · ·
· · · · · · · · · · · · · · · · · · · · · · · · abc
· · · · · · abb · · · · · · · · · · · · · · · abc
bbb · · · abb baa · · · · · · · · · · · · abc
· · · · · · abb · · · acc · · · · · · · · · abc
bbb ccc · · · baa · · · caa · · · · · · abc
· · · ccc abb baa · · · caa · · · · · · abc
bbb ccc abb baa · · · caa · · · · · · abc
· · · · · · abb baa acc caa · · · · · · abc
bbb · · · abb baa acc caa · · · · · · abc
bbb ccc abb baa acc caa · · · · · · abc
bbb · · · abb · · · acc · · · bcc · · · abc
bbb ccc abb · · · acc · · · bcc · · · abc
bbb · · · abb baa acc · · · bcc · · · abc
bbb ccc abb baa acc · · · bcc · · · abc
· · · · · · abb · · · · · · caa bcc · · · abc
· · · · · · abb · · · · · · caa bcc · · · abc
bbb · · · abb · · · · · · caa bcc · · · abc
bbb ccc abb · · · · · · caa bcc · · · abc
· · · · · · abb baa · · · caa bcc · · · abc
· · · · · · abb baa · · · caa bcc · · · abc
bbb · · · abb baa · · · caa bcc · · · abc
bbb · · · abb baa · · · caa bcc · · · abc
· · · ccc abb baa · · · caa bcc · · · abc
FINITE INTEGRAL RELATION ALGEBRAS
4865
4965
5065
5165
5265
5365
5465
5565
5665
5765
5865
5965
6065
6165
6265
6365
6465
6565
aaa
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
ccc
ccc
ccc
ccc
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
abb
abb
abb
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
23
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
9. Multiplication tables for the algebras 165 –6565
165
,
1
a
b
c
365
,
1
a
b
c
565
,
1
a
b
c
765
,
1
a
b
c
965
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
a
,
1
b
c
a
a
,
1
b
c
a
a
,
1
b
c
a
a
,
1
b
c
a
a
,
1b
ab
c
b
b
b
,
1a
c
b
b
b
,
1 ab
c
b
b
b
,
1a
c
b
b
b
,
1 ab
c
b
b
ab
,
1a
c
c
c
c
c
,
1 ab
c
c
c
c
,
1 ab
c
c
c
c
,
1 abc
c
c
c
c
,
1 abc
c
c
c
c
,
1 ab
265
,
1
a
b
c
465
,
1
a
b
c
665
,
1
a
b
c
865
,
1
a
b
c
1065
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
b
c
a
b
c
,
1a b
c
,
b 1a
c
,
c
c 1 ab
a
b
c
a
b
c
,
1a
b
c
,
b 1 ab
c
,
c
c
1 ab
a
b
c
a
b
c
,
1a b
c
,
b 1a
c
,
c
c 1 abc
a
b
c
a
b
c
,
1a
b
c
,
b 1 ab
c
,
c
c
1 abc
a
b
c
a
b
c
,
1 ab ab
c
,
ab 1 a
c
,
c
c 1 ab
24
ROGER D. MADDUX
1165
,
1
a
b
c
1365
,
1
a
b
c
1565
,
1
a
b
c
1765
,
1
a
b
c
1965
,
1
a
b
c
2165
,
1
a
b
c
2365
,
1
a
b
c
2565
,
1
a
b
c
2765
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
b
c
a
b
c
,
1 ab ab
c
,
ab 1 ab
c
,
c
c
1 ab
a
b
c
a
b
c
,
1 ab ab
c
,
ab 1 a
c
,
c
c 1 abc
a
b
c
a
b
c
,
1 bc a
ac
,
a
1
c
,
ac
c 1 ab
a
b
c
a
b
c
,
1 bc a
ac
,
a
1b
c
,
ac
c 1 ab
a
b
c
a
b
c
,
1 abc a
ac
,
a
1
c
,
ac
c 1 abc
a
b
c
a
b
c
,
1 bc ab
ac
,
ab 1 ac bc
,
ac
bc 1 ab
a
b
c
a
b
c
,
1 abc
ab
ac
,
ab
1 abc bc
,
ac
bc
1 ab
a b c
a b c
,
1 c b
,
c 1 a
,
b a 1
a
b
c
a
b
c
,
1 ab abc b
,
abc 1 ab a
,
b
a
1
1265
,
1
a
b
c
1465
,
1
a
b
c
1665
,
1
a
b
c
1865
,
1
a
b
c
2065
,
1
a
b
c
2265
,
1
a
b
c
2465
,
1
a
b
c
2665
,
1
a
b
c
2865
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
b
c
a
b
c
,
1 b ab
c
,
ab 1 a
c
,
c
c 1 abc
a
b
c
a
b
c
,
1 ab ab
c
,
ab 1 ab
c
,
c
c
1 abc
a
b
c
a
b
c
,
1 abc a
ac
,
a
1
c
,
ac
c 1 ab
a
b
c
a
b
c
,
1 abc a
ac
,
a
1b
c
,
ac
c 1 ab
a
b
c
a
b
c
,
1 abc a
ac
,
a
1b
c
,
ac
c 1 abc
a
b
c
a
b
c
,
1 abc ab
ac
,
ab
1 ac bc
,
ac
bc 1 ab
a
b
c
a
b
c
,
1 abc
ab
ac
,
ab
1 abc
bc
,
ac
bc
1 abc
a
b
c
a
b
c
,
1 a bc b
,
bc 1 a a
,
b
a 1
a
b
c
a
b
c
,
1 a bc bc
,
bc 1 a a
,
bc
a 1a
FINITE INTEGRAL RELATION ALGEBRAS
2965
,
1
a
b
c
3165
,
1
a
b
c
3365
,
1
a
b
c
3565
,
1
a
b
c
3765
,
1
a
b
c
3965
,
1
a
b
c
4165
,
1
a
b
c
4365
,
1
a
b
c
4565
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
b
c
a
b
c
,
1 abc ac ab
,
ac
1b a
,
ab
a 1c
a
b
c
a
b
c
,
1 abc abc ab
,
abc 1 ab a
,
ab
a
1c
a
b
c
a
b
c
,
1 abc abc abc
,
abc 1 ab a
,
abc
a
1a
a
b
c
a
b
c
,
1 a bc
bc
,
bc 1 ab ac
,
bc
ac 1 ab
a
b
c
a
b
c
,
1 ab abc
bc
,
abc 1 ab ac
,
bc
ac 1 ab
a
b
c
a
b
c
,
1 c bc ab
,
bc 1 a ac
,
ab ac 1 b
a
b
c
a
b
c
,
1 ac bc
ab
,
bc 1 ab ac
,
ab
ac 1 b
a
b
c
a
b
c
,
1 bc abc ab
,
abc 1 a ac
,
ab
ac 1 b
a
b
c
a
b
c
,
1 bc abc ab
,
abc 1 ab ac
,
ab
ac 1 b
3065
,
1
a
b
c
3265
,
1
a
b
c
3465
,
1
a
b
c
3665
,
1
a
b
c
3865
,
1
a
b
c
4065
,
1
a
b
c
4265
,
1
a
b
c
4465
,
1
a
b
c
4665
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
b
c
a
b
c
,
1 abc abc ab
,
abc 1 a a
,
ab
a 1c
a
b
c
a
b
c
,
1 abc abc abc
,
abc 1 a a
,
abc
a 1a
a
b
c
a
b
c
,
1 abc abc abc
,
abc 1 ab
a
,
abc
a
1 ac
a
b
c
a
b
c
,
1 a bc
bc
,
bc 1 ab
ac
,
bc
ac 1 abc
a
b
c
a
b
c
,
1 ab abc
bc
,
abc 1 ab
ac
,
bc
ac 1 abc
a
b
c
a
b
c
,
1 ac bc ab
,
bc 1 a ac
,
ab
ac 1 b
a
b
c
a
b
c
,
1 ac bc
ab
,
bc 1 ab ac
,
ab
ac 1 bc
a
b
c
a
b
c
,
1 abc abc ab
,
abc 1 a ac
,
ab
ac 1 b
a
b
c
a
b
c
,
1 abc abc ab
,
abc 1 ab ac
,
ab
ac 1 b
25
26
ROGER D. MADDUX
4765
,
1
a
b
c
4965
,
1
a
b
c
5165
,
1
a
b
c
5365
,
1
a
b
c
5565
,
1
a
b
c
5765
,
1
a
b
c
5965
,
1
a
b
c
6165
,
1
a
b
c
6365
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
a
,
1 bc
abc
ab
a
a
,
1 bc
abc
ab
a
a
,
1 bc
ac
abc
a
a
,
1 abc
ac
abc
a
a
,
1 abc
abc
abc
a
a
,
1 abc
abc
abc
a
a
,
1 abc
abc
abc
a
a
,
1 abc
abc
abc
a
a
,
1 abc
abc
abc
b
c
b
c
abc ab
,
1 a ac
,
ac 1 bc
b
c
b
c
abc
ab
,
1 ab ac
,
ac 1 bc
b
c
b
c
ac abc
,
1 b ac
,
ac 1 ab
b
c
b
c
ac
abc
,
1b
ac
,
ac 1 abc
b
c
b
c
abc abc
,
1 a ac
,
ac 1 ab
b
c
b
c
abc abc
,
1 ab ac
,
ac 1 ab
b
c
b
c
abc abc
,
1a
ac
,
ac 1 abc
b
c
b
c
abc
abc
,
1 ab
ac
,
ac 1 abc
b
c
b
c
abc abc
,
1 ac abc
,
abc 1 ab
4865
,
1
a
b
c
5065
,
1
a
b
c
5265
,
1
a
b
c
5465
,
1
a
b
c
5665
,
1
a
b
c
5865
,
1
a
b
c
6065
,
1
a
b
c
6265
,
1
a
b
c
6465
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
,
1
,
1
a
b
c
a
a
,
1 abc
abc
ab
a
a
,
1 abc
abc
ab
a
a
,
1 abc
ac
abc
a
a
,
1 bc
abc
abc
a
a
,
1 bc
abc
abc
a
a
,
1 bc
abc
abc
a
a
,
1 bc
abc
abc
a
a
,
1 bc
abc
abc
a
a
,
1 abc
abc
abc
b
c
b
c
abc ab
,
1 a ac
,
ac 1 bc
b
c
b
c
abc
ab
,
1 ab ac
,
ac 1 bc
b
c
b
c
ac abc
,
1 b ac
,
ac 1 ab
b
c
b
c
abc abc
,
1 a ac
,
ac 1 ab
b
c
b
c
abc abc
,
1 ab ac
,
ac 1 ab
b
c
b
c
abc abc
,
1a
ac
,
ac 1 abc
b
c
b
c
abc
abc
,
1 ab
ac
,
ac 1 abc
b
c
b
c
abc abc
,
1 ac abc
,
abc 1 ab
b
c
b
c
abc
abc
,
1 abc abc
,
abc 1 ab
FINITE INTEGRAL RELATION ALGEBRAS
6565
,
1
a
b
c
,
1
,
1
a
b
c
27
a
b
c
a
b
c
,
1 abc abc
abc
,
abc 1 abc abc
,
abc
abc 1 abc
10. Diversity cycles of the algebras 183 –8383
183
283
383
483
583
683
783
883
983
1083
1183
1283
1383
1483
1583
1683
1783
1883
1983
2083
2183
2283
2383
2483
2583
2683
2783
2883
2983
3083
3183
3283
3383
3483
3583
3683
3783
3883
3983
rrr
···
rrr
···
rrr
rrr
rrr
···
rrr
···
rrr
···
rrr
rrr
···
rrr
rrr
···
rrr
rrr
···
···
rrr
···
rrr
···
rrr
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr
···
rrr
···
sss
···
sss
sss
sss
···
sss
···
···
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
···
···
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
···
rrr̆
rrr̆
···
sss̆
···
···
···
···
sss̆
sss̆
sss̆
sss̆
sss̆
sss̆
···
···
···
···
···
···
sss̆
sss̆
sss̆
···
···
···
···
···
sss̆
sss̆
sss̆
sss̆
···
···
···
···
···
···
···
···
···
···
sss̆
rrs
···
···
···
···
···
···
···
···
···
···
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
···
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
···
···
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs̆
rrs̆
···
···
···
···
···
···
···
···
···
···
···
···
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
···
···
···
···
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
ssr
ssr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
···
···
···
···
···
···
ssr
ssr
ssr
ssr
ssr
ssr̆
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
···
···
···
···
···
···
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
srr
···
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
rsr
···
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rss srs
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
rss · · ·
28
ROGER D. MADDUX
4083
4183
4283
4383
4483
4583
4683
4783
4883
4983
5083
5183
5283
5383
5483
5583
5683
5783
5883
5983
6083
6183
6283
6383
6483
6583
6683
6783
6883
6983
7083
7183
7283
7383
7483
7583
7683
7783
7883
7983
8083
8183
8283
8383
rrr
rrr
···
rrr
rrr
rrr
rrr
rrr
···
rrr
···
rrr
···
rrr
···
rrr
···
rrr
rrr
rrr
rrr
rrr
···
rrr
rrr
···
rrr
rrr
···
rrr
rrr
···
rrr
···
rrr
···
rrr
rrr
rrr
rrr
···
rrr
···
rrr
rrr
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
sss
···
sss
sss
sss
···
···
sss
sss
sss
···
sss
sss
···
sss
sss
···
···
sss
sss
···
sss
···
sss
sss
···
···
sss
rrr̆
···
rrr̆
rrr̆
···
rrr̆
rrr̆
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
sss̆
sss̆
sss̆
sss̆
···
···
sss̆
···
···
···
···
···
···
···
sss̆
sss̆
sss̆
sss̆
···
···
···
···
sss̆
sss̆
sss̆
···
···
···
···
···
sss̆
sss̆
sss̆
sss̆
sss̆
sss̆
sss̆
···
···
···
···
···
sss̆
sss̆
sss̆
rrs
rrs
rrs
rrs
···
···
···
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
···
···
···
···
···
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs
rrs̆
rrs̆
rrs̆
rrs̆
···
···
···
···
···
···
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
···
···
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
rrs̆
ssr
ssr
ssr
ssr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr
ssr̆
ssr̆
ssr̆
ssr̆
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
ssr̆
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
srr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rsr
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
rss
11. Multiplication tables for algebras 183 –8383
srs
···
···
···
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
srs
FINITE INTEGRAL RELATION ALGEBRAS
,
183 1 r r̆ s s̆
, ,
1 1 r r̆ s s̆
,
r r s̆ 1 r̆ s
,
r̆ r̆ 1 s s̆ r
,
s s r̆ s̆ r 1
,
s̆ s̆ s r 1 r̆
,
383 1 r
r̆
s
s̆
, ,
1 1 r
r̆
s
s̆
,
r r r̆ 1 ss̆ r
r
,
r̆ r̆ 1 ss̆ r
r̆
r̆
,
s s r
r̆
s 1 ss̆
,
s̆ s̆ r
r̆ 1 ss̆ s̆
,
583 1
r
r̆
s s̆
, ,
1 1
r
r̆
s s̆
,
r r
r 1 rr̆ss̆ r r
,
r̆ r̆ 1 rr̆ss̆ r̆
r̆ r̆
,
s s
r
r̆
s̆ 1
,
s̆ s̆
r
r̆ 1 s
,
783 1 r
r̆ s s̆
, ,
1 1 r
r̆ s s̆
,
r r r̆ 1 ss̆ r r
,
r̆ r̆ 1 ss̆ r r̆ r̆
,
s s r
r̆ s̆ 1
,
s̆ s̆ r
r̆ 1 s
,
983 1 r
r̆
s
s̆
, ,
1 1 r
r̆
s
s̆
,
r r r̆ 1 ss̆ r
r
,
r̆ r̆ 1 ss̆ r
r̆
r̆
,
s s r
r̆ ss̆ 1 ss̆
,
s̆ s̆ r
r̆ 1 ss̆ ss̆
,
1183 1 r
r̆
s
s̆
, ,
1 1 r
r̆
s
s̆
,
r r s 1 ss̆ r rr̆
,
r̆ r̆ 1 ss̆ s̆ rr̆ r̆
,
s s r rr̆ s 1 ss̆
,
s̆ s̆ rr̆ r̆ 1 ss̆ s̆
,
1383 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rr̆s 1 rr̆ss̆ r rr̆
,
r̆ r̆ 1 rr̆ss̆ rr̆s̆ rr̆ r̆
,
s s
r
rr̆
s 1 ss̆
,
s̆ s̆ rr̆
r̆ 1 ss̆ s̆
,
1583 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rss̆ 1 rr̆ss̆ rr̆ rr̆
,
r̆ r̆ 1 rr̆ss̆ r̆ss̆ rr̆ rr̆
,
s s rr̆
rr̆
s 1 ss̆
,
s̆ s̆ rr̆
rr̆ 1 ss̆ s̆
,
283 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r
r 1 rr̆ss̆ r
r
,
r̆ r̆ 1 rr̆ss̆ r̆
r̆
r̆
,
s s
r
r̆
s 1 ss̆
,
s̆ s̆
r
r̆ 1 ss̆ s̆
,
483 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rr̆ 1 rr̆ss̆ r
r
,
r̆ r̆ 1 rr̆ss̆ rr̆
r̆
r̆
,
s s
r
r̆
s 1 ss̆
,
s̆ s̆
r
r̆ 1 ss̆ s̆
,
683 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r
r 1 rr̆ss̆ r
r
,
r̆ r̆ 1 rr̆ss̆ r̆
r̆
r̆
,
s s
r
r̆
ss̆ 1 ss̆
,
s̆ s̆
r
r̆ 1 ss̆ ss̆
,
883 1
r
r̆
s s̆
, ,
1 1
r
r̆
s s̆
,
r r rr̆ 1 rr̆ss̆ r r
,
r̆ r̆ 1 rr̆ss̆ rr̆ r̆ r̆
,
s s
r
r̆
s̆ 1
,
s̆ s̆
r
r̆ 1 s
,
1083 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rr̆ 1 rr̆ss̆ r
r
,
r̆ r̆ 1 rr̆ss̆ rr̆
r̆
r̆
,
s s
r
r̆
ss̆ 1 ss̆
,
s̆ s̆
r
r̆ 1 ss̆ ss̆
,
1283 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rs 1 rr̆ss̆ r rr̆
,
r̆ r̆ 1 rr̆ss̆ r̆s̆
rr̆ r̆
,
s s
r
rr̆
s 1 ss̆
,
s̆ s̆ rr̆
r̆ 1 ss̆ s̆
,
1483 1 r
r̆
s
s̆
, ,
1 1 r
r̆
s
s̆
,
r r ss̆ 1 ss̆ rr̆ rr̆
,
r̆ r̆ 1 ss̆ ss̆ rr̆ rr̆
,
s s rr̆ rr̆ s 1 ss̆
,
s̆ s̆ rr̆ rr̆ 1 ss̆ s̆
,
1683 1
r
r̆
s
s̆
, ,
1 1
r
r̆
s
s̆
,
r r rr̆ss̆ 1 rr̆ss̆ rr̆ rr̆
,
r̆ r̆ 1 rr̆ss̆ rr̆ss̆ rr̆ rr̆
,
s s rr̆
rr̆
s 1 ss̆
,
s̆ s̆ rr̆
rr̆ 1 ss̆ s̆
29
30
ROGER D. MADDUX
1783
,
1
r
r̆
s
s̆
1983
,
1
r
r̆
s
s̆
2183
,
1
r
r̆
s
s̆
2383
,
1
r
r̆
s
s̆
2583
,
1
r
r̆
s
s̆
2783
,
1
r
r̆
s
s̆
2983
,
1
r
r̆
s
s̆
3183
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆ rr̆
,
1 ss̆ ss̆ rr̆ rr̆
,
rr̆ rr̆ ss̆ 1 ss̆
,
rr̆ rr̆ 1 ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆ rr̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ rr̆
,
rr̆
rr̆
ss̆ 1 ss̆
,
rr̆
rr̆ 1 ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s̆ rr̆s
,
1 ss̆ ss̆ rr̆s̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆s 1 ss̆
,
rr̆s rr̆s 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s̆ rr̆s
,
1 ss̆ rss̆ rr̆s̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆s 1 ss̆
,
rr̆s rr̆s 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s̆ rr̆s
,
1 ss̆ ss̆ rr̆s̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆ss̆ 1 ss̆
,
rr̆s rr̆s 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s̆ rr̆s
,
1 ss̆ rss̆ rr̆s̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆ss̆ 1 ss̆
,
rr̆s rr̆s 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r 1 rr̆ss̆ rs
r
,
1 rr̆ss̆ r̆
r̆s
r̆
,
r
r̆
s 1 rr̆ss̆
,
rs̆
r̆s̆ 1 ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rs 1 rr̆ss̆ rs
rr̆
,
1 rr̆ss̆ r̆s̆ rr̆s
r̆
,
r
rr̆
s 1 rr̆ss̆
,
rr̆s̆
r̆s̆ 1 ss̆ s̆
1883
,
1
r
r̆
s
s̆
2083
,
1
r
r̆
s
s̆
2283
,
1
r
r̆
s
s̆
2483
,
1
r
r̆
s
s̆
2683
,
1
r
r̆
s
s̆
2883
,
1
r
r̆
s
s̆
3083
,
1
r
r̆
s
s̆
3283
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆ rr̆
,
1 rr̆ss̆ r̆ss̆ rr̆ rr̆
,
rr̆
rr̆
ss̆ 1 ss̆
,
rr̆
rr̆ 1 ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆s̆ 1 ss̆ rr̆ rs
,
1 ss̆ rs r̆s̆ rr̆
,
rr̆ r̆s̆ rs 1 ss̆
,
rs rr̆ 1 ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s̆ rr̆s
,
1 rr̆ss̆ r̆ss̆ rr̆s̆ rr̆s
,
rr̆s̆
rr̆s̆ rr̆s 1 ss̆
,
rr̆s
rr̆s 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s̆ rr̆s
,
1 rr̆ss̆ rr̆ss̆ rr̆s̆ rr̆s
,
rr̆s̆
rr̆s̆ rr̆s 1 ss̆
,
rr̆s
rr̆s 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s̆ rr̆s
,
1 rr̆ss̆ r̆ss̆ rr̆s̆ rr̆s
,
rr̆s̆
rr̆s̆ rr̆ss̆ 1 ss̆
,
rr̆s
rr̆s 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s̆ rr̆s
,
1 rr̆ss̆ rr̆ss̆ rr̆s̆ rr̆s
,
rr̆s̆
rr̆s̆ rr̆ss̆ 1 ss̆
,
rr̆s
rr̆s 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ 1 rr̆ss̆ rs
r
,
1 rr̆ss̆ rr̆
r̆s
r̆
,
r
r̆
s 1 rr̆ss̆
,
rs̆
r̆s̆ 1 ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆s 1 rr̆ss̆ rs
rr̆
,
1 rr̆ss̆ rr̆s̆ rr̆s
r̆
,
r
rr̆
s 1 rr̆ss̆
,
rr̆s̆
r̆s̆ 1 ss̆ s̆
FINITE INTEGRAL RELATION ALGEBRAS
3383
,
1
r
r̆
s
s̆
3583
,
1
r
r̆
s
s̆
3783
,
1
r
r̆
s
s̆
3983
,
1
r
r̆
s
s̆
4183
,
1
r
r̆
s
s̆
4383
,
1
r
r̆
s
s̆
4583
,
1
r
r̆
s
s̆
4783
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s rr̆
,
1 rr̆ss̆ r̆ss̆ rr̆s rr̆
,
rr̆
rr̆
s 1 rr̆ss̆
,
rr̆s̆
rr̆s̆ 1 ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆ss̆ rr̆s
,
1 ss̆ ss̆ rr̆ss̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆s 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆ss̆ rr̆s
,
1 ss̆ rss̆ rr̆ss̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆s 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆ss̆ rr̆s
,
1 ss̆ ss̆ rr̆ss̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆ss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆ss̆ rr̆s
,
1 ss̆ rss̆ rr̆ss̆ rr̆s
,
rr̆s̆ rr̆s̆ rr̆ss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 ss̆ rr̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r 1 rr̆ss̆ rs
rs̆
,
1 rr̆ss̆ r̆
r̆s
r̆s̆
,
rs
r̆s
s 1 rr̆ss̆
,
rs̆
r̆s̆ 1 rr̆ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ 1 rr̆ss̆ rs
rs̆
,
1 rr̆ss̆ rr̆
r̆s
r̆s̆
,
rs
r̆s
ss̆ 1 rr̆ss̆
,
rs̆
r̆s̆ 1 rr̆ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆s 1 ss̆ rs
rr̆s̆
,
1 ss̆ rs̆ rr̆s
r̆s̆
,
rs rr̆s
s 1 rr̆ss̆
,
rr̆s̆ r̆s̆ 1 rr̆ss̆ s̆
3483
,
1
r
r̆
s
s̆
3683
,
1
r
r̆
s
s̆
3883
,
1
r
r̆
s
s̆
4083
,
1
r
r̆
s
s̆
4283
,
1
r
r̆
s
s̆
4483
,
1
r
r̆
s
s̆
4683
,
1
r
r̆
s
s̆
4883
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r
rr̆ss̆
,
1 rr̆ss̆
rr̆
rr̆s̆
r
r
rss̆
,
1 rr̆ss̆
rr̆s̆
rr̆ss̆
r
r
rr̆ss̆
,
1 rr̆ss̆
rr̆s̆
rr̆ss̆
r
r
rss̆
,
1 rr̆ss̆
rr̆s̆
rr̆ss̆
r
r
rr̆ss̆
,
1 rr̆ss̆
rr̆s̆
rr̆ss̆
r
r
rr̆
,
1 rr̆ss̆
rs
rs̆
r
r
rs
,
1 rr̆ss̆
rs
rr̆s̆
r
r
rr̆s
,
1 rr̆ss̆
rs
rr̆s̆
r̆
r̆
,
1 rr̆ss̆
rr̆ss̆
rr̆
rr̆s̆
r̆
r̆
,
1 rr̆ss̆
r̆ss̆
rr̆s̆
rr̆ss̆
r̆
r̆
,
1 rr̆ss̆
rr̆ss̆
rr̆s̆
rr̆ss̆
r̆
r̆
,
1 rr̆ss̆
r̆ss̆
rr̆s̆
rr̆ss̆
r̆
r̆
,
1 rr̆ss̆
rr̆ss̆
rr̆s̆
rr̆ss̆
r̆
r̆
,
1 rr̆ss̆
rr̆
r̆s
r̆s̆
r̆
r̆
,
1 rr̆ss̆
r̆s̆
rr̆s
r̆s̆
r̆
r̆
,
1 rr̆ss̆
rr̆s̆
rr̆s
r̆s̆
31
s
s̆
s
s̆
rr̆s rr̆
rr̆s rr̆
,
s 1 rr̆ss̆
,
1 ss̆ s̆
s
s̆
s
s̆
rr̆ss̆ rr̆s
rr̆ss̆ rr̆s
,
rr̆s 1 rr̆ss̆
,
1 ss̆ rr̆s̆
s
s̆
s
s̆
rr̆ss̆ rr̆s
rr̆ss̆ rr̆s
,
rr̆s 1 rr̆ss̆
,
1 ss̆ rr̆s̆
s
s̆
s
s̆
rr̆ss̆ rr̆s
rr̆ss̆ rr̆s
,
rr̆ss̆ 1 rr̆ss̆
,
1 ss̆ rr̆ss̆
s
s̆
s
s̆
rr̆ss̆ rr̆s
rr̆ss̆ rr̆s
,
rr̆ss̆ 1 rr̆ss̆
,
1 ss̆ rr̆ss̆
s
s̆
s
s̆
rs
rs̆
r̆s
r̆s̆
,
s 1 rr̆ss̆
,
1 rr̆ss̆ s̆
s
s̆
s
s̆
rs
rr̆s̆
rr̆s
r̆s̆
,
s 1 rr̆ss̆
,
1 rr̆ss̆ s̆
s
s̆
s
s̆
rs
rr̆s̆
rr̆s
r̆s̆
,
s 1 rr̆ss̆
,
1 rr̆ss̆ s̆
32
ROGER D. MADDUX
4983
,
1
r
r̆
s
s̆
5183
,
1
r
r̆
s
s̆
5383
,
1
r
r̆
s
s̆
5583
,
1
r
r̆
s
s̆
5783
,
1
r
r̆
s
s̆
5983
,
1
r
r̆
s
s̆
6183
,
1
r
r̆
s
s̆
6383
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s
rr̆s̆
,
1 ss̆ ss̆ rr̆s
rr̆s̆
,
rr̆s rr̆s
s 1 rr̆ss̆
,
rr̆s̆ rr̆s̆ 1 rr̆ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s
rr̆s̆
,
1 ss̆ rss̆ rr̆s
rr̆s̆
,
rr̆s rr̆s
s 1 rr̆ss̆
,
rr̆s̆ rr̆s̆ 1 rr̆ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s
rr̆s̆
,
1 ss̆ ss̆ rr̆s
rr̆s̆
,
rr̆s rr̆s ss̆ 1 rr̆ss̆
,
rr̆s̆ rr̆s̆ 1 rr̆ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s
rr̆s̆
,
1 ss̆ rss̆ rr̆s
rr̆s̆
,
rr̆s rr̆s ss̆ 1 rr̆ss̆
,
rr̆s̆ rr̆s̆ 1 rr̆ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rs 1 rr̆ss̆ rs rr̆ss̆
,
1 rr̆ss̆ r̆s̆ rr̆ss̆ r̆s̆
,
rs
rr̆ss̆ r 1 rr̆
,
rr̆ss̆
r̆s̆ 1 rr̆ r̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rs̆ 1 rr̆ss̆ rr̆s
rss̆
,
1 rr̆ss̆ r̆s
r̆ss̆
rr̆s̆
,
rr̆s
r̆ss̆
rs 1 rr̆ss̆
,
rss̆
rr̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆s̆ 1 ss̆ rr̆s rss̆
,
1 ss̆ rs r̆ss̆ rr̆s̆
,
rr̆s r̆ss̆ rs̆ 1 rr̆
,
rss̆ rr̆s̆ 1 rr̆ r̆s
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆s̆ 1 rr̆ss̆ rr̆s
rss̆
,
1 rr̆ss̆ rr̆s
r̆ss̆
rr̆s̆
,
rr̆s
r̆ss̆
rss̆ 1 rr̆ss̆
,
rss̆
rr̆s̆ 1 rr̆ss̆ r̆ss̆
5083
,
1
r
r̆
s
s̆
5283
,
1
r
r̆
s
s̆
5483
,
1
r
r̆
s
s̆
5683
,
1
r
r̆
s
s̆
5883
,
1
r
r̆
s
s̆
6083
,
1
r
r̆
s
s̆
6283
,
1
r
r̆
s
s̆
6483
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s
rr̆s̆
,
1 rr̆ss̆ r̆ss̆
rr̆s
rr̆s̆
,
rr̆s
rr̆s
s 1 rr̆ss̆
,
rr̆s̆
rr̆s̆ 1 rr̆ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s
rr̆s̆
,
1 rr̆ss̆ rr̆ss̆ rr̆s
rr̆s̆
,
rr̆s
rr̆s
s 1 rr̆ss̆
,
rr̆s̆
rr̆s̆ 1 rr̆ss̆ s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s
rr̆s̆
,
1 rr̆ss̆ r̆ss̆
rr̆s
rr̆s̆
,
rr̆s
rr̆s
ss̆ 1 rr̆ss̆
,
rr̆s̆
rr̆s̆ 1 rr̆ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s
rr̆s̆
,
1 rr̆ss̆ rr̆ss̆ rr̆s
rr̆s̆
,
rr̆s
rr̆s
ss̆ 1 rr̆ss̆
,
rr̆s̆
rr̆s̆ 1 rr̆ss̆ ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rs 1 rr̆ss̆ rs
rr̆ss̆
,
1 rr̆ss̆ r̆s̆
rr̆ss̆
r̆s̆
,
rs
rr̆ss̆
rs 1 rr̆ss̆
,
rr̆ss̆
r̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆s̆ 1 rr̆ss̆ rr̆s
rss̆
,
1 rr̆ss̆ rr̆s
r̆ss̆
rr̆s̆
,
rr̆s
r̆ss̆
rs 1 rr̆ss̆
,
rss̆
rr̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆s̆ 1 rr̆ss̆ rr̆s rss̆
,
1 rr̆ss̆ rr̆s r̆ss̆ rr̆s̆
,
rr̆s
r̆ss̆ rs̆ 1 rr̆
,
rss̆
rr̆s̆ 1 rr̆ r̆s
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s rr̆ss̆
,
1 ss̆ ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rs 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆s̆
FINITE INTEGRAL RELATION ALGEBRAS
6583
,
1
r
r̆
s
s̆
6783
,
1
r
r̆
s
s̆
6983
,
1
r
r̆
s
s̆
7183
,
1
r
r̆
s
s̆
7383
,
1
r
r̆
s
s̆
7583
,
1
r
r̆
s
s̆
7783
,
1
r
r̆
s
s̆
7983
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ r̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆
rs 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s rr̆ss̆
,
1 ss̆ rss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rs 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ r̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rs̆ 1 rr̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ r̆s
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ r̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rs̆ 1 rr̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ r̆s
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆ss̆ rr̆ss̆
,
1 rr̆ss̆ r̆ss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆s 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ss̆ rr̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆ss̆ rr̆ss̆
,
1 ss̆ rss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆s 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ss̆ rr̆s̆
6683
,
1
r
r̆
s
s̆
6883
,
1
r
r̆
s
s̆
7083
,
1
r
r̆
s
s̆
7283
,
1
r
r̆
s
s̆
7483
,
1
r
r̆
s
s̆
7683
,
1
r
r̆
s
s̆
7883
,
1
r
r̆
s
s̆
8083
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ r 1 rr̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ r̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆s rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆
rs 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
ss̆ 1 ss̆ rr̆s rr̆ss̆
,
1 ss̆ ss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s rr̆ss̆
,
1 ss̆ rss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rs̆ 1 rr̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ r̆s
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆s rr̆ss̆
,
1 ss̆ rss̆ rr̆ss̆ rr̆s̆
,
rr̆s rr̆ss̆ rss̆ 1 rr̆ss̆
,
rr̆ss̆ rr̆s̆ 1 rr̆ss̆ r̆ss̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rss̆ 1 rr̆ss̆ rr̆ss̆ rr̆ss̆
,
1 rr̆ss̆ r̆ss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆ 1 rr̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ rr̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆ss̆ rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆ 1 rr̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ rr̆
r
r̆
s
s̆
r
r̆
s
s̆
,
rr̆ss̆ 1 rr̆ss̆ rr̆ss̆ rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆s 1 rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ss̆ rr̆s̆
33
34
ROGER D. MADDUX
8183
,
1
r
r̆
s
s̆
8383
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r̆
s
s̆
r
r̆
s
s̆
,
r̆ss̆ 1 ss̆ rr̆ss̆ rr̆ss̆
,
1 ss̆ rss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ rr̆s̆ 1 rr̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ rr̆s
r
r̆
s
r
r̆
s
,
rr̆ss̆ 1 rr̆ss̆ rr̆ss̆
,
1 rr̆ss̆ rr̆ss̆ rr̆ss̆
rr̆ss̆ rr̆ss̆ rr̆ss̆
,
rr̆ss̆ rr̆ss̆ 1 rr̆ss̆
8283
,
1
r
r̆
s
s̆
,
1
,
1
r
r̆
s
s̆
r
r
rr̆ss̆
,
1 rr̆ss̆
rr̆ss̆
rr̆ss̆
r̆
r̆
,
1 rr̆ss̆
rr̆ss̆
rr̆ss̆
rr̆ss̆
s
s
rr̆ss̆
rr̆ss̆
rr̆s̆
,
1 rr̆
s̆
s̆
rr̆ss̆
rr̆ss̆
,
1 rr̆
rr̆s
s̆
s̆
rr̆ss̆
rr̆ss̆
,
1 rr̆ss̆
rr̆ss̆
12. Failures of (J), (L), (M) among 11 –183
The formulas (J), (L), and (M) hold in all 13 of the algebras 11 , 12 , 22 , 13 –33 ,
and 17 –77 . Among the 185 algebras 137 –3737 , 165 –6565 , and 183 –8383 there are 48
in which at least one of (J), (L), and (M) fail to hold. This is proved in the table
below. Suppose A is one of the algebras 137 –3737 , 165 –6565 , and 183 –8383 . If A
does not appear in the table, then (J), (L), and (M) hold in A. Suppose A does
appear in the table.
- If the entry in the (J)-column is tuvwxyz, then (J) fails to hold in A when
x01 = t,
x02 = u,
x03 = w,
x24 = y,
x21 = v,
x31 = x,
x43 = z.
- If the entry in the (L)-column is tuvwxyz, then t ≤ u;v · w ;x · y ;z and (L)
fails to hold in A when
x02 = u,
x03 = w,
x04 = y,
x21 = v,
x31 = x,
x41 = z.
- If the entry in the (M)-column is tuvwxyz, then (M) fails to hold in A when
x01 = t,
x02 = u,
x03 = w,
x24 = y,
x21 = v,
x32 = x,
x41 = z.
- If there is no entry, then the corresponding formula holds in the algebra A.
Failures of (J), (L), (M) among the 4329 algebras 11316 –13161316 and 13013 –30133013
are given in §18 below.
alg.
(J)
(L)
(M)
alg.
(J)
(L)
(M)
1437 arr̆r̆raa
arr̆aaaa 1637 arr̆r̆raa raaarr̆r̆ arr̆aaaa
2137
rar̆r̆r̆r̆r̆ 2437
aaarrr̆r̆
2537 raaar̆rr raaar̆r̆r̆ rr̆r̆aaar 2637 raaar̆rr
aaarrr̆r̆
2737 raaar̆r̆a raaarr̆a arr̆aaaa 2937 raaar̆r̆a raaarr̆a arr̆aaaa
3437 aarrrrr aarrrr̆r aarr̆r̆r̆a 2165 aabccbb
aabccbc
2265 aabccbb
aabccbc 2365 aacbbcc
aabccbc
FINITE INTEGRAL RELATION ALGEBRAS
alg.
3565
3765
4165
4365
4865
5065
5865
1883
2383
2583
2783
3583
3983
4783
5183
5583
6783
7283
(J)
(L)
aaaaccb
aabbbcb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
srrrs̆ss
srrrs̆ss
srrrs̆s̆r
srrrs̆s̆r
rr̆sss̆r̆r
rr̆r̆r̆sr̆s̆
srrrs̆s̆s̆
rr̆r̆r̆sss
srrrss̆r
srrrss̆r
srrrsss
srrrss̆s̆
rrsr̆sss
rr̆sssss̆
(M)
babbcbb
aabccac
aaaacbc
aabbbca
abccccc
abccccc
rr̆sr̆r̆r̆r̆
rr̆r̆rsrs̆
ss̆s̆rrrs
rr̆r̆rsrs̆
rss̆rrrr
rss̆rrrr
rrs̆r̆r̆r̆r̆
rss̆rrr̆r
rss̆rrr̆r
srs̆r̆s̆r̆r̆
rrss̆srr
alg.
3665
4065
4265
4765
4965
5465
1583
2283
2483
2683
2883
3783
4183
4983
5383
6483
7083
8183
35
(J)
(L)
aaaaccb
aaaaccb
aabbbcb
aaaaccb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
srrrs̆ss
srrrs̆ss
srrrs̆s̆r
srrrs̆s̆r
rss̆s̆srr
rss̆s̆srr
rr̆r̆r̆ss̆r̆
rr̆r̆r̆ss̆r̆
srrrss̆s̆
(M)
babbcbb
aaaacbc
aaaacbc
aabbbca
abcaacc
rr̆sr̆r̆r̆r̆
rrrsss̆s̆
rrrsss̆s̆
rrrsss̆s̆
rrrsss̆s̆
rss̆rrr̆r
rss̆rrr̆r
rss̆rrrr
rss̆rrrr
rss̆r̆r̆rr
rss̆r̆r̆rr
rr̆sss̆r̆s
13. Independence of (J), (L), and (M)
It can be seen from Table 4 that (J), (L), and (M) are independent, in the sense
that there are relation algebras which satisfy two of (J), (L), and (M) but not the
third. Indeed, Table 4 shows that every possible combination of (J), (L), and (M)
can hold or fail in some relation algebra. For independence we must look at the
columns labelled J, L, and M. It is apparent that the “easiest” independence to
,
prove is that of (M) from (J) and (L). Among the 37 algebras with atoms 1 , a, r, r̆
there are two which satisfy (J) and (L) but not (M), and there are 6 such algebras
,
among the 65 that have atoms 1 , a, b, c. For the independence of (J) from (L) and
(M) we need to use algebra with at least five atoms, and there are total of 169
that work. However, among the 4527 integral relation algebras with five or fewer
atoms, there are only two that satisfy both (J) and (M) but fail to satisfy (L).
They are algebra 27933013 , which has 17 cycles, and algebra 27953013 , which has 18
, , ,
,
,
,
cycles. The 17 cycles of algebra 27933013 are [1 , 1 , 1 ], [1 , a, a], [1 , b, b], [1 , c, c],
,
[1 , d, d], [a, b, b], [a, a, c], [a, c, c], [b, b, c], [a, a, d], [a, d, d], [b, b, d], [c, c, d], [c, d, d],
[a, b, c], [a, b, d], and [b, c, d]. The 18 cycles of algebra 27953013 are those of 27933013
plus [b, b, b]. The multiplication tables of the atoms of these two algebras are shown
in Figure 10.
14. 5-dimensional relational basis data for 198 algebras
In this section we give data on the existence of 5-dimensional relational bases
for each the 198 algebras 11 , 12 , 22 , 13 –33 , 17 –77 , 137 –3737 , 165 –6565 , and 183 –8383 .
To see how to read the table below, consider an example. The entries for algebra
57 in columns headed “a”, “c”, “q”, “b”, and “f ” are 3, 2, 3, 1, and 2, respectively.
This means that the number of atoms of 57 is a = 3, the number of cycles of 57 is
c = 2, the number of permutation-equivalence classes of matrices in B4 (57 ) is q = 3,
the number of permutation-equivalence classes of matrices in B4 (57 ) that appear
as minors in the maximum 5-dimensional relational basis is b = 1, and the number
36
ROGER D. MADDUX
Algebra 27933013 :
;
a
,
a 1 cd
b bcd
c abc
d abd
b
bcd
,
1 acd
abd
abc
Algebra 27953013 :
c
d
abc abd
abd abc
,
1 ad bcd
,
bcd 1 ac
;
a
,
a 1 cd
b bcd
c abc
d abd
b
bcd
,
1 abcd
abd
abc
c
d
abc abd
abd abc
,
1 ad bcd
,
bcd 1 ac
Figure 10. Two algebras that satisfy (J) and (M) but not (L)
of permutation-equivalence classes of forbidden matrices in B4 (57 ) is f = 2. If an
algebra A has no entry in the “f ”-column, then f = 0, q = b, A has no forbidden
4-by-4 matrices in B4 A, and the maximum 5-dimensional relational basis of A is all
of B5 A. Whenever f 6= 0, the algebra has a proper 5-dimensional relational basis.
A similar table for the algebras 11316 –13161316 and 13013 –30133013 appears below.
alg.
11
13
17
47
77
337
637
937
1237
1537
1837
2137
2437
2737
3037
3337
3637
265
565
865
1165
1465
1765
2065
2365
2665
2965
3265
3565
3865
4165
a
1
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
c
0
1
1
3
4
3
5
2
4
5
1
5
4
4
6
6
6
4
4
6
6
7
5
7
8
3
6
6
6
8
6
q
0
1
1
5
11
2
12
2
9
16
1
16
11
13
26
32
33
8
8
14
18
21
12
22
32
6
16
25
19
33
16
b
0
1
1
5
11
2
12
2
9
16
1
0
0
0
26
32
33
8
8
14
18
21
10
22
0
6
16
25
0
0
0
f alg.
12
23
27
57
137
437
737
1037
1337
1637
1937
2237
2537
2837
3137
3437
3737
365
665
965
1265
1565
2 1865
2165
2465
2765
3065
3365
3665
3965
4265
a
2
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
c
0
1
2
2
3
4
2
3
4
5
3
6
4
5
5
5
7
4
5
4
5
4
6
6
9
5
6
7
7
4
7
q
0
0
3
3
5
5
3
4
9
15
7
23
13
19
18
13
42
8
11
8
11
9
17
18
39
16
20
30
23
8
20
b
0
0
3
1
5
5
3
4
9
0
7
23
0
0
18
0
42
8
11
6
9
7
17
0
39
16
20
30
0
4
0
f alg.
22
33
37
2 67
237
537
837
1137
1437
1737
2037
2337
2637
2937
3237
3537
165
465
765
2 1065
2 1365
2 1665
1965
2265
2565
2865
3165
3465
3765
4 4065
4365
a
2
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
c
1
2
2
3
4
4
3
3
4
6
4
3
5
5
5
6
3
5
5
5
6
5
6
7
1
4
7
8
7
5
5
q
1
4
3
7
8
9
5
7
10
21
9
8
16
20
23
22
5
11
11
13
16
14
19
25
1
11
25
35
29
12
15
b
1
4
3
7
8
9
5
7
0
20
9
8
0
0
22
22
5
11
11
13
16
14
19
0
1
11
25
35
0
0
0
f
1
1
FINITE INTEGRAL RELATION ALGEBRAS
alg.
4465
4765
5065
5365
5665
5965
6265
6565
383
683
983
1283
1583
1883
2183
2483
2783
3083
3383
3683
3983
4283
4583
4883
5183
5483
5783
6083
6383
6683
6983
7283
7583
7883
8183
a
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
b f alg.
6 22
0
4565
6 19
0
4865
8 33
0
5165
8 36 36
5465
7 31 27 4 5765
8 41 41
6065
7 36 36
6365
10 66 66
183
4
5
5
483
5 13 13
783
5 10 10
1083
5 15 15
1383
6 27
0
1683
7 34
0
1983
7 36 36
2283
9 72
0
2583
9 50
0
2883
6 19 19
3183
7 39
0
3483
9 87
0
3783
9 70
0
4083
11 120 120
4383
8 36 34 2 4683
8 50 50
4983
8 44
0
5283
9 69 61 8 5583
7 41 41
5883
9 69 55 14 6183
10 81 81
6483
9 79 79
6783
9 70 70
7083
9 47
0
7383
11 122 122
7683
10 112 112
7983
10 74
0
8283
a
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
b
6 22
0
7 26
0
6 22 18
6 24
0
8 41 41
8 38 35
8 46 46
2
1
1
5 12 12
4
4
4
6 17 17
6 21 21
7 37 37
8 44 44
8 58
0
8 45
0
10 81
0
6 24 24
8 52 52
9 64
0
10 102 102
6 24 24
7 40 40
7 37
0
9 77 77
9 52
0
8 64 64
8 29 21
8 58
0
9 67
0
9 72
0
10 88 88
9 90 88
10 103 103
11 125 125
f alg.
4665
4965
4 5265
5565
5865
3 6165
6465
283
583
883
1183
1483
1783
2083
2383
2683
2983
3283
3583
3883
4183
4483
4783
5083
5383
5683
5983
8 6283
6583
6883
7183
7483
2 7783
8083
8383
a
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
37
c
7
7
7
7
7
9
9
4
4
5
4
5
6
6
8
9
5
7
8
10
10
7
7
8
8
10
8
9
9
10
10
10
10
11
12
q
29
26
29
34
31
48
56
8
7
11
8
17
24
16
41
67
14
32
55
105
79
30
28
61
45
85
57
55
90
108
104
81
132
154
176
b f
29
0
29
34
0
48
56
8
7
11
8
17
24
16
0
0
14
32
0
0
0
28 2
0
61
0
77 8
43 14
0
84 6
108
104
0
132
154
176
15. The number of finite integral relation algebras
Suppose G(n, s) and H(n, s) are real-valued functions of n, s ∈ ω. We say that
G(n, s) approaches H(n, s) and write G(n, s) ∼ H(n, s) if for every real number
r > 0 there is some N ∈ ω such that if N < n ∈ ω, 1 ≤ s ≤ n, and n − s is even,
then
G(n, s)
|1 −
| < r.
H(n, s)
Let
Q(n, s) =
1
(n − 1)((n − 1)2 + 3s − 1)
6
38
ROGER D. MADDUX
n
s Q(n, s) P (n, s)
1
2
3
3
4
4
5
5
5
6
6
6
1
2
1
3
2
4
1
3
5
2
4
6
0
1
2
4
7
10
12
16
20
25
30
35
2Q(n,s)
P (n,s)
F (n, s)
1
1.00
1
1
2.00
2
2
2.00
3
2
8.00
7
2
64.00
37
6
170.66
65
8
512.00
83
4
16384.00
1316
24
43690.66
3013
8
4194304.00
47865
12 89478485.33 988464
120 286331153.07 3849920
F (n,s)P (n,s)
2Q(n,s)
1.000000
1.000000
1.500000
0.875000
0.578125
0.380859
0.162109
0.080322
0.068539
0.011412
0.011047
0.013446
Table 21. Expected and actual numbers of finite relation algebras
and
1
1
(n − s) !2 2 (n−s)
P (n, s) = (s − 1)!
2
whenever s ≤ n ∈ ω and n − s is even. Let F (n, s) be the number of isomorphism
types of integral relation algebras with n atoms and s symmetric atoms.
Theorem 1 (Maddux [18]). An asymptotic formula for the number of finite integral
relation algebras with n atoms and s symmetric atoms:
2
1
F (n, s) ∼
2 6 (n−1)((n−1) +3s−1)
2Q(n,s)
=
1
P (n, s)
(s − 1)! 12 (n − s) !2 2 (n−s)
Some numerical data is shown in Table 21. According to Th. 1, the number in
the rightmost column of the table below should be approaching 1 as n gets large.
It is interesting to note that until n = s = 6 the values are actually getting smaller
as n and s increase.
16. Cycles of algebras 11316 –13161316
11316
21316
31316
41316
51316
61316
71316
81316
91316
101316
111316
121316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb baa arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
abb · · · arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
···
···
···
···
···
···
···
···
···
···
···
···
rbb rra rrb
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
abr
···
···
···
···
···
···
···
···
···
···
···
···
bar
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
131316
141316
151316
161316
171316
181316
191316
201316
211316
221316
231316
241316
251316
261316
271316
281316
291316
301316
311316
321316
331316
341316
351316
361316
371316
381316
391316
401316
411316
421316
431316
441316
451316
461316
471316
481316
491316
501316
511316
521316
531316
541316
551316
561316
571316
581316
591316
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
39
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb rra rrb
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
··· ··· ···
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
rbb · · · · · ·
abr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
40
ROGER D. MADDUX
601316
611316
621316
631316
641316
651316
661316
671316
681316
691316
701316
711316
721316
731316
741316
751316
761316
771316
781316
791316
801316
811316
821316
831316
841316
851316
861316
871316
881316
891316
901316
911316
921316
931316
941316
951316
961316
971316
981316
991316
1001316
1011316
1021316
1031316
1041316
1051316
1061316
aaa
aaa
aaa
···
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
···
···
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
···
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
···
···
bbb
···
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
···
rar
rar
rar
rar
rar
rar
···
···
···
···
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra rrb
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
1071316
1081316
1091316
1101316
1111316
1121316
1131316
1141316
1151316
1161316
1171316
1181316
1191316
1201316
1211316
1221316
1231316
1241316
1251316
1261316
1271316
1281316
1291316
1301316
1311316
1321316
1331316
1341316
1351316
1361316
1371316
1381316
1391316
1401316
1411316
1421316
1431316
1441316
1451316
1461316
1471316
1481316
1491316
1501316
1511316
1521316
1531316
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
···
···
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
41
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
42
ROGER D. MADDUX
1541316
1551316
1561316
1571316
1581316
1591316
1601316
1611316
1621316
1631316
1641316
1651316
1661316
1671316
1681316
1691316
1701316
1711316
1721316
1731316
1741316
1751316
1761316
1771316
1781316
1791316
1801316
1811316
1821316
1831316
1841316
1851316
1861316
1871316
1881316
1891316
1901316
1911316
1921316
1931316
1941316
1951316
1961316
1971316
1981316
1991316
2001316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
···
···
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
abb
abb
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
brr
brr
brr
brr
brr
brr
···
···
rbr
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
2011316
2021316
2031316
2041316
2051316
2061316
2071316
2081316
2091316
2101316
2111316
2121316
2131316
2141316
2151316
2161316
2171316
2181316
2191316
2201316
2211316
2221316
2231316
2241316
2251316
2261316
2271316
2281316
2291316
2301316
2311316
2321316
2331316
2341316
2351316
2361316
2371316
2381316
2391316
2401316
2411316
2421316
2431316
2441316
2451316
2461316
2471316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
···
aaa
···
aaa
aaa
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
···
bbb
···
···
bbb
bbb
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
abb
···
abb
abb
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
baa
baa
baa
baa
···
baa
···
···
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
brr
brr
brr
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
43
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
44
ROGER D. MADDUX
2481316
2491316
2501316
2511316
2521316
2531316
2541316
2551316
2561316
2571316
2581316
2591316
2601316
2611316
2621316
2631316
2641316
2651316
2661316
2671316
2681316
2691316
2701316
2711316
2721316
2731316
2741316
2751316
2761316
2771316
2781316
2791316
2801316
2811316
2821316
2831316
2841316
2851316
2861316
2871316
2881316
2891316
2901316
2911316
2921316
2931316
2941316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
arr
arr
arr
arr
arr
arr
···
···
···
···
arr
arr
arr
arr
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
2951316
2961316
2971316
2981316
2991316
3001316
3011316
3021316
3031316
3041316
3051316
3061316
3071316
3081316
3091316
3101316
3111316
3121316
3131316
3141316
3151316
3161316
3171316
3181316
3191316
3201316
3211316
3221316
3231316
3241316
3251316
3261316
3271316
3281316
3291316
3301316
3311316
3321316
3331316
3341316
3351316
3361316
3371316
3381316
3391316
3401316
3411316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
45
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
46
ROGER D. MADDUX
3421316
3431316
3441316
3451316
3461316
3471316
3481316
3491316
3501316
3511316
3521316
3531316
3541316
3551316
3561316
3571316
3581316
3591316
3601316
3611316
3621316
3631316
3641316
3651316
3661316
3671316
3681316
3691316
3701316
3711316
3721316
3731316
3741316
3751316
3761316
3771316
3781316
3791316
3801316
3811316
3821316
3831316
3841316
3851316
3861316
3871316
3881316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
bbb
···
···
bbb
bbb
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
rrr̆
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
3891316
3901316
3911316
3921316
3931316
3941316
3951316
3961316
3971316
3981316
3991316
4001316
4011316
4021316
4031316
4041316
4051316
4061316
4071316
4081316
4091316
4101316
4111316
4121316
4131316
4141316
4151316
4161316
4171316
4181316
4191316
4201316
4211316
4221316
4231316
4241316
4251316
4261316
4271316
4281316
4291316
4301316
4311316
4321316
4331316
4341316
4351316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
···
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
rrr
···
···
···
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
rrr̆
···
···
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
47
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
48
ROGER D. MADDUX
4361316
4371316
4381316
4391316
4401316
4411316
4421316
4431316
4441316
4451316
4461316
4471316
4481316
4491316
4501316
4511316
4521316
4531316
4541316
4551316
4561316
4571316
4581316
4591316
4601316
4611316
4621316
4631316
4641316
4651316
4661316
4671316
4681316
4691316
4701316
4711316
4721316
4731316
4741316
4751316
4761316
4771316
4781316
4791316
4801316
4811316
4821316
aaa
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
bbb
···
···
bbb
···
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr
···
rrr
rrr
···
rrr
···
···
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra rrb
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
4831316
4841316
4851316
4861316
4871316
4881316
4891316
4901316
4911316
4921316
4931316
4941316
4951316
4961316
4971316
4981316
4991316
5001316
5011316
5021316
5031316
5041316
5051316
5061316
5071316
5081316
5091316
5101316
5111316
5121316
5131316
5141316
5151316
5161316
5171316
5181316
5191316
5201316
5211316
5221316
5231316
5241316
5251316
5261316
5271316
5281316
5291316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
arr
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
49
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
50
ROGER D. MADDUX
5301316
5311316
5321316
5331316
5341316
5351316
5361316
5371316
5381316
5391316
5401316
5411316
5421316
5431316
5441316
5451316
5461316
5471316
5481316
5491316
5501316
5511316
5521316
5531316
5541316
5551316
5561316
5571316
5581316
5591316
5601316
5611316
5621316
5631316
5641316
5651316
5661316
5671316
5681316
5691316
5701316
5711316
5721316
5731316
5741316
5751316
5761316
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
abb
abb
···
···
abb
abb
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
brr
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
5771316
5781316
5791316
5801316
5811316
5821316
5831316
5841316
5851316
5861316
5871316
5881316
5891316
5901316
5911316
5921316
5931316
5941316
5951316
5961316
5971316
5981316
5991316
6001316
6011316
6021316
6031316
6041316
6051316
6061316
6071316
6081316
6091316
6101316
6111316
6121316
6131316
6141316
6151316
6161316
6171316
6181316
6191316
6201316
6211316
6221316
6231316
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
51
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
52
ROGER D. MADDUX
6241316
6251316
6261316
6271316
6281316
6291316
6301316
6311316
6321316
6331316
6341316
6351316
6361316
6371316
6381316
6391316
6401316
6411316
6421316
6431316
6441316
6451316
6461316
6471316
6481316
6491316
6501316
6511316
6521316
6531316
6541316
6551316
6561316
6571316
6581316
6591316
6601316
6611316
6621316
6631316
6641316
6651316
6661316
6671316
6681316
6691316
6701316
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
brr
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
6711316
6721316
6731316
6741316
6751316
6761316
6771316
6781316
6791316
6801316
6811316
6821316
6831316
6841316
6851316
6861316
6871316
6881316
6891316
6901316
6911316
6921316
6931316
6941316
6951316
6961316
6971316
6981316
6991316
7001316
7011316
7021316
7031316
7041316
7051316
7061316
7071316
7081316
7091316
7101316
7111316
7121316
7131316
7141316
7151316
7161316
7171316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
53
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
54
ROGER D. MADDUX
7181316
7191316
7201316
7211316
7221316
7231316
7241316
7251316
7261316
7271316
7281316
7291316
7301316
7311316
7321316
7331316
7341316
7351316
7361316
7371316
7381316
7391316
7401316
7411316
7421316
7431316
7441316
7451316
7461316
7471316
7481316
7491316
7501316
7511316
7521316
7531316
7541316
7551316
7561316
7571316
7581316
7591316
7601316
7611316
7621316
7631316
7641316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
baa
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra rrb
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
rra · · ·
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
7651316
7661316
7671316
7681316
7691316
7701316
7711316
7721316
7731316
7741316
7751316
7761316
7771316
7781316
7791316
7801316
7811316
7821316
7831316
7841316
7851316
7861316
7871316
7881316
7891316
7901316
7911316
7921316
7931316
7941316
7951316
7961316
7971316
7981316
7991316
8001316
8011316
8021316
8031316
8041316
8051316
8061316
8071316
8081316
8091316
8101316
8111316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
rrr
···
rrr
···
rrr
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
rrr̆
···
···
rrr̆
rrr̆
···
···
rrr̆
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
···
···
abb
abb
···
···
abb
abb
···
···
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
55
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
56
ROGER D. MADDUX
8121316
8131316
8141316
8151316
8161316
8171316
8181316
8191316
8201316
8211316
8221316
8231316
8241316
8251316
8261316
8271316
8281316
8291316
8301316
8311316
8321316
8331316
8341316
8351316
8361316
8371316
8381316
8391316
8401316
8411316
8421316
8431316
8441316
8451316
8461316
8471316
8481316
8491316
8501316
8511316
8521316
8531316
8541316
8551316
8561316
8571316
8581316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
8591316
8601316
8611316
8621316
8631316
8641316
8651316
8661316
8671316
8681316
8691316
8701316
8711316
8721316
8731316
8741316
8751316
8761316
8771316
8781316
8791316
8801316
8811316
8821316
8831316
8841316
8851316
8861316
8871316
8881316
8891316
8901316
8911316
8921316
8931316
8941316
8951316
8961316
8971316
8981316
8991316
9001316
9011316
9021316
9031316
9041316
9051316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
rar
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
57
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
58
ROGER D. MADDUX
9061316
9071316
9081316
9091316
9101316
9111316
9121316
9131316
9141316
9151316
9161316
9171316
9181316
9191316
9201316
9211316
9221316
9231316
9241316
9251316
9261316
9271316
9281316
9291316
9301316
9311316
9321316
9331316
9341316
9351316
9361316
9371316
9381316
9391316
9401316
9411316
9421316
9431316
9441316
9451316
9461316
9471316
9481316
9491316
9501316
9511316
9521316
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
9531316
9541316
9551316
9561316
9571316
9581316
9591316
9601316
9611316
9621316
9631316
9641316
9651316
9661316
9671316
9681316
9691316
9701316
9711316
9721316
9731316
9741316
9751316
9761316
9771316
9781316
9791316
9801316
9811316
9821316
9831316
9841316
9851316
9861316
9871316
9881316
9891316
9901316
9911316
9921316
9931316
9941316
9951316
9961316
9971316
9981316
9991316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
59
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
60
10001316
10011316
10021316
10031316
10041316
10051316
10061316
10071316
10081316
10091316
10101316
10111316
10121316
10131316
10141316
10151316
10161316
10171316
10181316
10191316
10201316
10211316
10221316
10231316
10241316
10251316
10261316
10271316
10281316
10291316
10301316
10311316
10321316
10331316
10341316
10351316
10361316
10371316
10381316
10391316
10401316
10411316
10421316
10431316
10441316
10451316
10461316
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
rrr
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
10471316
10481316
10491316
10501316
10511316
10521316
10531316
10541316
10551316
10561316
10571316
10581316
10591316
10601316
10611316
10621316
10631316
10641316
10651316
10661316
10671316
10681316
10691316
10701316
10711316
10721316
10731316
10741316
10751316
10761316
10771316
10781316
10791316
10801316
10811316
10821316
10831316
10841316
10851316
10861316
10871316
10881316
10891316
10901316
10911316
10921316
10931316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
rrr
rrr
···
···
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
61
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa rbb rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
raa · · · rra rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
62
10941316
10951316
10961316
10971316
10981316
10991316
11001316
11011316
11021316
11031316
11041316
11051316
11061316
11071316
11081316
11091316
11101316
11111316
11121316
11131316
11141316
11151316
11161316
11171316
11181316
11191316
11201316
11211316
11221316
11231316
11241316
11251316
11261316
11271316
11281316
11291316
11301316
11311316
11321316
11331316
11341316
11351316
11361316
11371316
11381316
11391316
11401316
ROGER D. MADDUX
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
brr
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rbr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
···
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
rrb abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
11411316
11421316
11431316
11441316
11451316
11461316
11471316
11481316
11491316
11501316
11511316
11521316
11531316
11541316
11551316
11561316
11571316
11581316
11591316
11601316
11611316
11621316
11631316
11641316
11651316
11661316
11671316
11681316
11691316
11701316
11711316
11721316
11731316
11741316
11751316
11761316
11771316
11781316
11791316
11801316
11811316
11821316
11831316
11841316
11851316
11861316
11871316
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
rrr̆
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
63
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
64
11881316
11891316
11901316
11911316
11921316
11931316
11941316
11951316
11961316
11971316
11981316
11991316
12001316
12011316
12021316
12031316
12041316
12051316
12061316
12071316
12081316
12091316
12101316
12111316
12121316
12131316
12141316
12151316
12161316
12171316
12181316
12191316
12201316
12211316
12221316
12231316
12241316
12251316
12261316
12271316
12281316
12291316
12301316
12311316
12321316
12331316
12341316
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
rrr
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
···
···
···
···
···
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
FINITE INTEGRAL RELATION ALGEBRAS
12351316
12361316
12371316
12381316
12391316
12401316
12411316
12421316
12431316
12441316
12451316
12461316
12471316
12481316
12491316
12501316
12511316
12521316
12531316
12541316
12551316
12561316
12571316
12581316
12591316
12601316
12611316
12621316
12631316
12641316
12651316
12661316
12671316
12681316
12691316
12701316
12711316
12721316
12731316
12741316
12751316
12761316
12771316
12781316
12791316
12801316
12811316
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
rrr
···
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
···
···
···
···
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
65
rbr
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
66
ROGER D. MADDUX
12821316
12831316
12841316
12851316
12861316
12871316
12881316
12891316
12901316
12911316
12921316
12931316
12941316
12951316
12961316
12971316
12981316
12991316
13001316
13011316
13021316
13031316
13041316
13051316
13061316
13071316
13081316
13091316
13101316
13111316
13121316
13131316
13141316
13151316
13161316
aaa
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
bbb
···
bbb
bbb
···
···
bbb
···
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
rrr
···
···
rrr
rrr
rrr
rrr
···
···
···
···
rrr
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
···
···
···
rrr
rrr
rrr
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
···
···
···
···
···
···
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
rrr̆
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
arr
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
rar
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
brr
rbr
···
···
···
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
rbr
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
raa
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rbb
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rra
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
rrb
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
abr
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bar
bdd dbb cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
dcc
···
···
···
···
···
···
···
···
17. Cycles of algebras 13013 –30133013
13013
23013
33013
43013
53013
63013
73013
83013
aaa bbb ccc ddd
··· ··· ··· ···
aaa · · · · · · · · ·
· · · bbb · · · · · ·
aaa bbb · · · · · ·
· · · · · · ccc · · ·
aaa · · · ccc · · ·
· · · bbb ccc · · ·
aaa bbb ccc · · ·
abb baa acc
abb · · · acc
abb · · · acc
abb · · · acc
abb · · · acc
abb · · · acc
abb · · · acc
abb · · · acc
abb · · · acc
caa
···
···
···
···
···
···
···
···
add daa bcc cbb
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
abc
···
···
···
···
···
···
···
···
abd
···
···
···
···
···
···
···
···
acd
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
93013
103013
113013
123013
133013
143013
153013
163013
173013
183013
193013
203013
213013
223013
233013
243013
253013
263013
273013
283013
293013
303013
313013
323013
333013
343013
353013
363013
373013
383013
393013
403013
413013
423013
433013
443013
453013
463013
473013
483013
493013
503013
513013
523013
533013
543013
553013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
···
bbb
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
67
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
68
ROGER D. MADDUX
563013
573013
583013
593013
603013
613013
623013
633013
643013
653013
663013
673013
683013
693013
703013
713013
723013
733013
743013
753013
763013
773013
783013
793013
803013
813013
823013
833013
843013
853013
863013
873013
883013
893013
903013
913013
923013
933013
943013
953013
963013
973013
983013
993013
1003013
1013013
1023013
aaa
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
···
aaa
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
bbb
bbb
···
···
bbb
···
···
bbb
bbb
bbb
···
···
bbb
bbb
bbb
···
···
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
bbb
ccc
ccc
···
···
···
ccc
···
···
···
···
ccc
ccc
···
···
ccc
···
···
···
ccc
ccc
ccc
···
ccc
···
···
···
ccc
ccc
···
···
···
···
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
ddd
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
···
···
···
···
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
···
···
···
···
···
···
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc abd
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
1033013
1043013
1053013
1063013
1073013
1083013
1093013
1103013
1113013
1123013
1133013
1143013
1153013
1163013
1173013
1183013
1193013
1203013
1213013
1223013
1233013
1243013
1253013
1263013
1273013
1283013
1293013
1303013
1313013
1323013
1333013
1343013
1353013
1363013
1373013
1383013
1393013
1403013
1413013
1423013
1433013
1443013
1453013
1463013
1473013
1483013
1493013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
···
ccc
···
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
add · · · bcc · · ·
69
bdd dbb cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc abd
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
70
ROGER D. MADDUX
1503013
1513013
1523013
1533013
1543013
1553013
1563013
1573013
1583013
1593013
1603013
1613013
1623013
1633013
1643013
1653013
1663013
1673013
1683013
1693013
1703013
1713013
1723013
1733013
1743013
1753013
1763013
1773013
1783013
1793013
1803013
1813013
1823013
1833013
1843013
1853013
1863013
1873013
1883013
1893013
1903013
1913013
1923013
1933013
1943013
1953013
1963013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
ccc
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
···
···
···
ccc
···
···
···
···
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
···
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd dbb
· · · bdd · · ·
· · · bdd · · ·
· · · bdd · · ·
· · · bdd · · ·
· · · bdd · · ·
· · · bdd · · ·
· · · bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
cbb bdd · · ·
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
· · · · · · dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc abd
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
1973013
1983013
1993013
2003013
2013013
2023013
2033013
2043013
2053013
2063013
2073013
2083013
2093013
2103013
2113013
2123013
2133013
2143013
2153013
2163013
2173013
2183013
2193013
2203013
2213013
2223013
2233013
2243013
2253013
2263013
2273013
2283013
2293013
2303013
2313013
2323013
2333013
2343013
2353013
2363013
2373013
2383013
2393013
2403013
2413013
2423013
2433013
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
···
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa add daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
71
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb cdd
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc abd
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
abc · · ·
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
72
ROGER D. MADDUX
2443013
2453013
2463013
2473013
2483013
2493013
2503013
2513013
2523013
2533013
2543013
2553013
2563013
2573013
2583013
2593013
2603013
2613013
2623013
2633013
2643013
2653013
2663013
2673013
2683013
2693013
2703013
2713013
2723013
2733013
2743013
2753013
2763013
2773013
2783013
2793013
2803013
2813013
2823013
2833013
2843013
2853013
2863013
2873013
2883013
2893013
2903013
aaa
aaa
aaa
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
···
aaa
aaa
aaa
aaa
···
···
aaa
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
···
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
···
···
bbb
bbb
···
···
bbb
bbb
ccc
···
···
ccc
···
···
···
ccc
···
···
···
ccc
···
···
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
···
···
ccc
ccc
ccc
ccc
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
···
ddd
ddd
···
ddd
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
···
ddd
···
ddd
···
ddd
···
ddd
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
···
···
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
caa
add
···
···
···
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
bdd
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd dcc abc abd
· · · dcc abc · · ·
· · · dcc abc · · ·
· · · dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd dcc abc · · ·
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
cdd · · · abc abd
acd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
2913013
2923013
2933013
2943013
2953013
2963013
2973013
2983013
2993013
3003013
3013013
3023013
3033013
3043013
3053013
3063013
3073013
3083013
3093013
3103013
3113013
3123013
3133013
3143013
3153013
3163013
3173013
3183013
3193013
3203013
3213013
3223013
3233013
3243013
3253013
3263013
3273013
3283013
3293013
3303013
3313013
3323013
3333013
3343013
3353013
3363013
3373013
aaa
aaa
aaa
aaa
aaa
···
···
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
···
···
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
bbb
···
bbb
···
bbb
···
···
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
···
···
bbb
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
ccc
ddd abb baa acc caa add
· · · abb baa · · · caa add
· · · abb baa · · · caa add
ddd abb baa · · · caa add
ddd abb baa · · · caa add
· · · · · · · · · · · · caa add
ddd · · · · · · · · · caa add
· · · abb · · · · · · caa add
· · · abb · · · · · · caa add
ddd abb · · · · · · caa add
ddd abb · · · · · · caa add
· · · abb baa · · · caa add
· · · abb baa · · · caa add
· · · abb baa · · · caa add
ddd abb baa · · · caa add
ddd abb baa · · · caa add
ddd abb baa · · · caa add
· · · · · · · · · · · · caa · · ·
· · · · · · · · · · · · caa · · ·
ddd · · · · · · · · · caa · · ·
ddd · · · · · · · · · caa · · ·
· · · · · · baa · · · caa · · ·
· · · · · · baa · · · caa · · ·
ddd · · · baa · · · caa · · ·
ddd · · · baa · · · caa · · ·
· · · abb baa · · · caa · · ·
· · · abb baa · · · caa · · ·
· · · abb baa · · · caa · · ·
· · · abb baa · · · caa · · ·
ddd abb baa · · · caa · · ·
ddd abb baa · · · caa · · ·
ddd abb baa · · · caa · · ·
ddd abb baa · · · caa · · ·
· · · · · · · · · acc caa add
· · · · · · · · · acc caa add
ddd · · · · · · acc caa add
ddd · · · · · · acc caa add
· · · abb · · · acc caa add
· · · abb · · · acc caa add
ddd abb · · · acc caa add
ddd abb · · · acc caa add
· · · abb baa acc caa add
· · · abb baa acc caa add
ddd abb baa acc caa add
ddd abb baa acc caa add
· · · · · · · · · acc caa add
· · · · · · · · · acc caa add
· · · · · · · · · acc caa add
73
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd acd
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
74
ROGER D. MADDUX
3383013
3393013
3403013
3413013
3423013
3433013
3443013
3453013
3463013
3473013
3483013
3493013
3503013
3513013
3523013
3533013
3543013
3553013
3563013
3573013
3583013
3593013
3603013
3613013
3623013
3633013
3643013
3653013
3663013
3673013
3683013
3693013
3703013
3713013
3723013
3733013
3743013
3753013
3763013
3773013
3783013
3793013
3803013
3813013
3823013
3833013
3843013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ccc
ddd
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
abb
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
· · · dbb
· · · dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd acd
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
abd · · ·
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
3853013
3863013
3873013
3883013
3893013
3903013
3913013
3923013
3933013
3943013
3953013
3963013
3973013
3983013
3993013
4003013
4013013
4023013
4033013
4043013
4053013
4063013
4073013
4083013
4093013
4103013
4113013
4123013
4133013
4143013
4153013
4163013
4173013
4183013
4193013
4203013
4213013
4223013
4233013
4243013
4253013
4263013
4273013
4283013
4293013
4303013
4313013
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
bbb
···
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
···
abb
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
75
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
bdd dbb cdd dcc abc abd acd
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
· · · dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
bdd dbb cdd dcc abc abd · · ·
· · · · · · · · · · · · abc abd acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
76
ROGER D. MADDUX
4323013
4333013
4343013
4353013
4363013
4373013
4383013
4393013
4403013
4413013
4423013
4433013
4443013
4453013
4463013
4473013
4483013
4493013
4503013
4513013
4523013
4533013
4543013
4553013
4563013
4573013
4583013
4593013
4603013
4613013
4623013
4633013
4643013
4653013
4663013
4673013
4683013
4693013
4703013
4713013
4723013
4733013
4743013
4753013
4763013
4773013
4783013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
···
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
···
···
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ddd
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
4793013
4803013
4813013
4823013
4833013
4843013
4853013
4863013
4873013
4883013
4893013
4903013
4913013
4923013
4933013
4943013
4953013
4963013
4973013
4983013
4993013
5003013
5013013
5023013
5033013
5043013
5053013
5063013
5073013
5083013
5093013
5103013
5113013
5123013
5133013
5143013
5153013
5163013
5173013
5183013
5193013
5203013
5213013
5223013
5233013
5243013
5253013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
77
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb cdd
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
78
ROGER D. MADDUX
5263013
5273013
5283013
5293013
5303013
5313013
5323013
5333013
5343013
5353013
5363013
5373013
5383013
5393013
5403013
5413013
5423013
5433013
5443013
5453013
5463013
5473013
5483013
5493013
5503013
5513013
5523013
5533013
5543013
5553013
5563013
5573013
5583013
5593013
5603013
5613013
5623013
5633013
5643013
5653013
5663013
5673013
5683013
5693013
5703013
5713013
5723013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
···
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ddd
···
···
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
5733013
5743013
5753013
5763013
5773013
5783013
5793013
5803013
5813013
5823013
5833013
5843013
5853013
5863013
5873013
5883013
5893013
5903013
5913013
5923013
5933013
5943013
5953013
5963013
5973013
5983013
5993013
6003013
6013013
6023013
6033013
6043013
6053013
6063013
6073013
6083013
6093013
6103013
6113013
6123013
6133013
6143013
6153013
6163013
6173013
6183013
6193013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
ccc
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
ccc
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ddd
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
79
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc cbb
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bdd dbb cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
80
ROGER D. MADDUX
6203013
6213013
6223013
6233013
6243013
6253013
6263013
6273013
6283013
6293013
6303013
6313013
6323013
6333013
6343013
6353013
6363013
6373013
6383013
6393013
6403013
6413013
6423013
6433013
6443013
6453013
6463013
6473013
6483013
6493013
6503013
6513013
6523013
6533013
6543013
6553013
6563013
6573013
6583013
6593013
6603013
6613013
6623013
6633013
6643013
6653013
6663013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
bbb
···
bbb
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
···
···
ccc
···
···
ccc
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
6673013
6683013
6693013
6703013
6713013
6723013
6733013
6743013
6753013
6763013
6773013
6783013
6793013
6803013
6813013
6823013
6833013
6843013
6853013
6863013
6873013
6883013
6893013
6903013
6913013
6923013
6933013
6943013
6953013
6963013
6973013
6983013
6993013
7003013
7013013
7023013
7033013
7043013
7053013
7063013
7073013
7083013
7093013
7103013
7113013
7123013
7133013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
bbb
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
ccc
···
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
81
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
82
ROGER D. MADDUX
7143013
7153013
7163013
7173013
7183013
7193013
7203013
7213013
7223013
7233013
7243013
7253013
7263013
7273013
7283013
7293013
7303013
7313013
7323013
7333013
7343013
7353013
7363013
7373013
7383013
7393013
7403013
7413013
7423013
7433013
7443013
7453013
7463013
7473013
7483013
7493013
7503013
7513013
7523013
7533013
7543013
7553013
7563013
7573013
7583013
7593013
7603013
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
ccc
ccc
ccc
···
···
···
ccc
ccc
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
abb
abb
abb
···
···
abb
abb
···
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
baa
baa
baa
···
baa
···
···
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
caa
caa
caa
···
···
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb bdd
add daa bcc cbb bdd
add daa bcc cbb bdd
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
dbb cdd
· · · cdd
· · · cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dbb cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
7613013
7623013
7633013
7643013
7653013
7663013
7673013
7683013
7693013
7703013
7713013
7723013
7733013
7743013
7753013
7763013
7773013
7783013
7793013
7803013
7813013
7823013
7833013
7843013
7853013
7863013
7873013
7883013
7893013
7903013
7913013
7923013
7933013
7943013
7953013
7963013
7973013
7983013
7993013
8003013
8013013
8023013
8033013
8043013
8053013
8063013
8073013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
···
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
···
···
···
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
···
···
···
83
daa
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
84
ROGER D. MADDUX
8083013
8093013
8103013
8113013
8123013
8133013
8143013
8153013
8163013
8173013
8183013
8193013
8203013
8213013
8223013
8233013
8243013
8253013
8263013
8273013
8283013
8293013
8303013
8313013
8323013
8333013
8343013
8353013
8363013
8373013
8383013
8393013
8403013
8413013
8423013
8433013
8443013
8453013
8463013
8473013
8483013
8493013
8503013
8513013
8523013
8533013
8543013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ddd abb baa acc
· · · abb · · · · · ·
· · · · · · baa · · ·
· · · · · · baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
· · · abb · · · · · ·
· · · abb · · · · · ·
· · · abb · · · · · ·
· · · abb · · · · · ·
· · · · · · baa · · ·
· · · · · · baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
· · · abb baa · · ·
ddd abb · · · · · ·
ddd abb · · · · · ·
ddd abb · · · · · ·
ddd abb · · · · · ·
ddd · · · baa · · ·
ddd · · · baa · · ·
ddd abb baa · · ·
ddd abb baa · · ·
ddd abb baa · · ·
ddd abb baa · · ·
· · · abb · · · acc
· · · abb · · · acc
· · · abb · · · acc
· · · abb · · · acc
ddd abb · · · acc
ddd abb · · · acc
ddd abb · · · acc
ddd abb · · · acc
· · · · · · baa acc
· · · · · · baa acc
· · · · · · baa acc
· · · · · · baa acc
ddd · · · baa acc
ddd · · · baa acc
ddd · · · baa acc
ddd · · · baa acc
· · · abb baa acc
· · · abb baa acc
· · · abb baa acc
· · · abb baa acc
caa
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add daa bcc cbb bdd
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
· · · · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
add · · · bcc cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
8553013
8563013
8573013
8583013
8593013
8603013
8613013
8623013
8633013
8643013
8653013
8663013
8673013
8683013
8693013
8703013
8713013
8723013
8733013
8743013
8753013
8763013
8773013
8783013
8793013
8803013
8813013
8823013
8833013
8843013
8853013
8863013
8873013
8883013
8893013
8903013
8913013
8923013
8933013
8943013
8953013
8963013
8973013
8983013
8993013
9003013
9013013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
85
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
86
ROGER D. MADDUX
9023013
9033013
9043013
9053013
9063013
9073013
9083013
9093013
9103013
9113013
9123013
9133013
9143013
9153013
9163013
9173013
9183013
9193013
9203013
9213013
9223013
9233013
9243013
9253013
9263013
9273013
9283013
9293013
9303013
9313013
9323013
9333013
9343013
9353013
9363013
9373013
9383013
9393013
9403013
9413013
9423013
9433013
9443013
9453013
9463013
9473013
9483013
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc caa
acc caa
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
add daa bcc cbb bdd
add · · · bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
· · · daa bcc cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
9493013
9503013
9513013
9523013
9533013
9543013
9553013
9563013
9573013
9583013
9593013
9603013
9613013
9623013
9633013
9643013
9653013
9663013
9673013
9683013
9693013
9703013
9713013
9723013
9733013
9743013
9753013
9763013
9773013
9783013
9793013
9803013
9813013
9823013
9833013
9843013
9853013
9863013
9873013
9883013
9893013
9903013
9913013
9923013
9933013
9943013
9953013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ddd
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa add daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
· · · · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
87
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
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···
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···
···
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···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
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···
···
88
9963013
9973013
9983013
9993013
10003013
10013013
10023013
10033013
10043013
10053013
10063013
10073013
10083013
10093013
10103013
10113013
10123013
10133013
10143013
10153013
10163013
10173013
10183013
10193013
10203013
10213013
10223013
10233013
10243013
10253013
10263013
10273013
10283013
10293013
10303013
10313013
10323013
10333013
10343013
10353013
10363013
10373013
10383013
10393013
10403013
10413013
10423013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
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···
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···
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···
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···
aaa
aaa
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aaa
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···
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···
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···
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···
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···
aaa
aaa
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aaa
aaa
aaa
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···
aaa
···
aaa
bbb
···
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···
···
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···
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···
···
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···
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···
···
bbb
bbb
···
···
bbb
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···
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···
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···
bbb
···
bbb
···
···
bbb
bbb
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
···
···
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···
···
···
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
10433013
10443013
10453013
10463013
10473013
10483013
10493013
10503013
10513013
10523013
10533013
10543013
10553013
10563013
10573013
10583013
10593013
10603013
10613013
10623013
10633013
10643013
10653013
10663013
10673013
10683013
10693013
10703013
10713013
10723013
10733013
10743013
10753013
10763013
10773013
10783013
10793013
10803013
10813013
10823013
10833013
10843013
10853013
10863013
10873013
10883013
10893013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
89
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
90
10903013
10913013
10923013
10933013
10943013
10953013
10963013
10973013
10983013
10993013
11003013
11013013
11023013
11033013
11043013
11053013
11063013
11073013
11083013
11093013
11103013
11113013
11123013
11133013
11143013
11153013
11163013
11173013
11183013
11193013
11203013
11213013
11223013
11233013
11243013
11253013
11263013
11273013
11283013
11293013
11303013
11313013
11323013
11333013
11343013
11353013
11363013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ddd
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
11373013
11383013
11393013
11403013
11413013
11423013
11433013
11443013
11453013
11463013
11473013
11483013
11493013
11503013
11513013
11523013
11533013
11543013
11553013
11563013
11573013
11583013
11593013
11603013
11613013
11623013
11633013
11643013
11653013
11663013
11673013
11683013
11693013
11703013
11713013
11723013
11733013
11743013
11753013
11763013
11773013
11783013
11793013
11803013
11813013
11823013
11833013
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
91
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
···
···
···
···
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
92
11843013
11853013
11863013
11873013
11883013
11893013
11903013
11913013
11923013
11933013
11943013
11953013
11963013
11973013
11983013
11993013
12003013
12013013
12023013
12033013
12043013
12053013
12063013
12073013
12083013
12093013
12103013
12113013
12123013
12133013
12143013
12153013
12163013
12173013
12183013
12193013
12203013
12213013
12223013
12233013
12243013
12253013
12263013
12273013
12283013
12293013
12303013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ddd
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
daa bcc cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
daa · · · cbb bdd dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
12313013
12323013
12333013
12343013
12353013
12363013
12373013
12383013
12393013
12403013
12413013
12423013
12433013
12443013
12453013
12463013
12473013
12483013
12493013
12503013
12513013
12523013
12533013
12543013
12553013
12563013
12573013
12583013
12593013
12603013
12613013
12623013
12633013
12643013
12653013
12663013
12673013
12683013
12693013
12703013
12713013
12723013
12733013
12743013
12753013
12763013
12773013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
93
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
94
12783013
12793013
12803013
12813013
12823013
12833013
12843013
12853013
12863013
12873013
12883013
12893013
12903013
12913013
12923013
12933013
12943013
12953013
12963013
12973013
12983013
12993013
13003013
13013013
13023013
13033013
13043013
13053013
13063013
13073013
13083013
13093013
13103013
13113013
13123013
13133013
13143013
13153013
13163013
13173013
13183013
13193013
13203013
13213013
13223013
13233013
13243013
ROGER D. MADDUX
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
ccc
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
add · · · bcc cbb bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
13253013
13263013
13273013
13283013
13293013
13303013
13313013
13323013
13333013
13343013
13353013
13363013
13373013
13383013
13393013
13403013
13413013
13423013
13433013
13443013
13453013
13463013
13473013
13483013
13493013
13503013
13513013
13523013
13533013
13543013
13553013
13563013
13573013
13583013
13593013
13603013
13613013
13623013
13633013
13643013
13653013
13663013
13673013
13683013
13693013
13703013
13713013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
95
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
96
13723013
13733013
13743013
13753013
13763013
13773013
13783013
13793013
13803013
13813013
13823013
13833013
13843013
13853013
13863013
13873013
13883013
13893013
13903013
13913013
13923013
13933013
13943013
13953013
13963013
13973013
13983013
13993013
14003013
14013013
14023013
14033013
14043013
14053013
14063013
14073013
14083013
14093013
14103013
14113013
14123013
14133013
14143013
14153013
14163013
14173013
14183013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ddd
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc caa
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
acc · · ·
add daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
· · · daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
14193013
14203013
14213013
14223013
14233013
14243013
14253013
14263013
14273013
14283013
14293013
14303013
14313013
14323013
14333013
14343013
14353013
14363013
14373013
14383013
14393013
14403013
14413013
14423013
14433013
14443013
14453013
14463013
14473013
14483013
14493013
14503013
14513013
14523013
14533013
14543013
14553013
14563013
14573013
14583013
14593013
14603013
14613013
14623013
14633013
14643013
14653013
aaa
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caa
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add daa
· · · daa
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97
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abc
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abc
abc
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abc
abc
abc
abc
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abc
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abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
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98
14663013
14673013
14683013
14693013
14703013
14713013
14723013
14733013
14743013
14753013
14763013
14773013
14783013
14793013
14803013
14813013
14823013
14833013
14843013
14853013
14863013
14873013
14883013
14893013
14903013
14913013
14923013
14933013
14943013
14953013
14963013
14973013
14983013
14993013
15003013
15013013
15023013
15033013
15043013
15053013
15063013
15073013
15083013
15093013
15103013
15113013
15123013
ROGER D. MADDUX
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acc
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caa add daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
caa · · · daa
bcc
bcc
bcc
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···
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abc
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abc
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abc
abc
abc
abc
abc
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abd
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acd
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acd
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acd
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acd
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acd
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acd
acd
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bcd
···
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···
FINITE INTEGRAL RELATION ALGEBRAS
15133013
15143013
15153013
15163013
15173013
15183013
15193013
15203013
15213013
15223013
15233013
15243013
15253013
15263013
15273013
15283013
15293013
15303013
15313013
15323013
15333013
15343013
15353013
15363013
15373013
15383013
15393013
15403013
15413013
15423013
15433013
15443013
15453013
15463013
15473013
15483013
15493013
15503013
15513013
15523013
15533013
15543013
15553013
15563013
15573013
15583013
15593013
aaa
···
aaa
···
aaa
···
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···
aaa
···
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···
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···
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···
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···
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···
aaa
aaa
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···
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···
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···
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···
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···
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···
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···
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···
bbb
···
···
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···
···
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···
···
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···
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···
···
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···
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···
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···
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···
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···
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···
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···
···
bbb
bbb
···
···
bbb
ccc
ccc
ccc
ccc
ccc
···
···
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···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
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ccc
ccc
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···
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···
ccc
ccc
ccc
ddd
ddd
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···
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···
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···
ddd
ddd
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···
···
ddd
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···
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···
ddd
ddd
ddd
ddd
···
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···
ddd
ddd
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ddd
···
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···
abb
···
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···
abb
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abb
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baa
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baa
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baa
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···
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···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
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···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
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···
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···
···
add
···
···
···
···
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···
···
···
···
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···
···
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···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
99
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
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daa
daa
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daa
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daa
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daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
100
15603013
15613013
15623013
15633013
15643013
15653013
15663013
15673013
15683013
15693013
15703013
15713013
15723013
15733013
15743013
15753013
15763013
15773013
15783013
15793013
15803013
15813013
15823013
15833013
15843013
15853013
15863013
15873013
15883013
15893013
15903013
15913013
15923013
15933013
15943013
15953013
15963013
15973013
15983013
15993013
16003013
16013013
16023013
16033013
16043013
16053013
16063013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ddd
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc caa add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
· · · · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
acc · · · add daa bcc cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
16073013
16083013
16093013
16103013
16113013
16123013
16133013
16143013
16153013
16163013
16173013
16183013
16193013
16203013
16213013
16223013
16233013
16243013
16253013
16263013
16273013
16283013
16293013
16303013
16313013
16323013
16333013
16343013
16353013
16363013
16373013
16383013
16393013
16403013
16413013
16423013
16433013
16443013
16453013
16463013
16473013
16483013
16493013
16503013
16513013
16523013
16533013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
101
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
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···
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···
···
···
···
···
···
···
···
···
102
16543013
16553013
16563013
16573013
16583013
16593013
16603013
16613013
16623013
16633013
16643013
16653013
16663013
16673013
16683013
16693013
16703013
16713013
16723013
16733013
16743013
16753013
16763013
16773013
16783013
16793013
16803013
16813013
16823013
16833013
16843013
16853013
16863013
16873013
16883013
16893013
16903013
16913013
16923013
16933013
16943013
16953013
16963013
16973013
16983013
16993013
17003013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
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···
aaa
···
aaa
···
aaa
···
aaa
···
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···
aaa
···
aaa
···
aaa
···
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···
aaa
···
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···
aaa
···
aaa
···
aaa
···
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···
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···
aaa
···
aaa
bbb
···
bbb
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···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
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···
···
bbb
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···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
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···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
17013013
17023013
17033013
17043013
17053013
17063013
17073013
17083013
17093013
17103013
17113013
17123013
17133013
17143013
17153013
17163013
17173013
17183013
17193013
17203013
17213013
17223013
17233013
17243013
17253013
17263013
17273013
17283013
17293013
17303013
17313013
17323013
17333013
17343013
17353013
17363013
17373013
17383013
17393013
17403013
17413013
17423013
17433013
17443013
17453013
17463013
17473013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
···
bbb
bbb
···
bbb
···
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
···
ccc
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
103
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
104
17483013
17493013
17503013
17513013
17523013
17533013
17543013
17553013
17563013
17573013
17583013
17593013
17603013
17613013
17623013
17633013
17643013
17653013
17663013
17673013
17683013
17693013
17703013
17713013
17723013
17733013
17743013
17753013
17763013
17773013
17783013
17793013
17803013
17813013
17823013
17833013
17843013
17853013
17863013
17873013
17883013
17893013
17903013
17913013
17923013
17933013
17943013
ROGER D. MADDUX
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ddd
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
abb
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
· · · · · · bcc cbb bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
17953013
17963013
17973013
17983013
17993013
18003013
18013013
18023013
18033013
18043013
18053013
18063013
18073013
18083013
18093013
18103013
18113013
18123013
18133013
18143013
18153013
18163013
18173013
18183013
18193013
18203013
18213013
18223013
18233013
18243013
18253013
18263013
18273013
18283013
18293013
18303013
18313013
18323013
18333013
18343013
18353013
18363013
18373013
18383013
18393013
18403013
18413013
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
···
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb
· · · · · · bcc cbb
· · · · · · bcc cbb
· · · · · · bcc cbb
· · · · · · bcc cbb
· · · · · · bcc cbb
· · · · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
add · · · bcc cbb
105
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
abd acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
106
18423013
18433013
18443013
18453013
18463013
18473013
18483013
18493013
18503013
18513013
18523013
18533013
18543013
18553013
18563013
18573013
18583013
18593013
18603013
18613013
18623013
18633013
18643013
18653013
18663013
18673013
18683013
18693013
18703013
18713013
18723013
18733013
18743013
18753013
18763013
18773013
18783013
18793013
18803013
18813013
18823013
18833013
18843013
18853013
18863013
18873013
18883013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add daa bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
add · · · bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
· · · daa bcc cbb bdd dbb cdd dcc abc abd acd
bcd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
FINITE INTEGRAL RELATION ALGEBRAS
18893013
18903013
18913013
18923013
18933013
18943013
18953013
18963013
18973013
18983013
18993013
19003013
19013013
19023013
19033013
19043013
19053013
19063013
19073013
19083013
19093013
19103013
19113013
19123013
19133013
19143013
19153013
19163013
19173013
19183013
19193013
19203013
19213013
19223013
19233013
19243013
19253013
19263013
19273013
19283013
19293013
19303013
19313013
19323013
19333013
19343013
19353013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ccc
···
ccc
ccc
ccc
ccc
···
···
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
ddd
···
ddd
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
abb
···
abb
···
···
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
···
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
acc
acc
acc
···
···
···
···
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
···
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
107
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
bdd dbb
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
···
···
···
···
···
···
···
···
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
108
19363013
19373013
19383013
19393013
19403013
19413013
19423013
19433013
19443013
19453013
19463013
19473013
19483013
19493013
19503013
19513013
19523013
19533013
19543013
19553013
19563013
19573013
19583013
19593013
19603013
19613013
19623013
19633013
19643013
19653013
19663013
19673013
19683013
19693013
19703013
19713013
19723013
19733013
19743013
19753013
19763013
19773013
19783013
19793013
19803013
19813013
19823013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
bbb
ccc
ccc
···
···
ccc
ccc
···
ccc
···
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
ccc
···
ccc
···
ccc
ccc
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
abb
···
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
···
···
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
add daa bcc cbb bdd
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
· · · · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
add · · · bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
· · · daa bcc · · · · · ·
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
19833013
19843013
19853013
19863013
19873013
19883013
19893013
19903013
19913013
19923013
19933013
19943013
19953013
19963013
19973013
19983013
19993013
20003013
20013013
20023013
20033013
20043013
20053013
20063013
20073013
20083013
20093013
20103013
20113013
20123013
20133013
20143013
20153013
20163013
20173013
20183013
20193013
20203013
20213013
20223013
20233013
20243013
20253013
20263013
20273013
20283013
20293013
aaa
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
abb
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
acc
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
109
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc cbb
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
110
20303013
20313013
20323013
20333013
20343013
20353013
20363013
20373013
20383013
20393013
20403013
20413013
20423013
20433013
20443013
20453013
20463013
20473013
20483013
20493013
20503013
20513013
20523013
20533013
20543013
20553013
20563013
20573013
20583013
20593013
20603013
20613013
20623013
20633013
20643013
20653013
20663013
20673013
20683013
20693013
20703013
20713013
20723013
20733013
20743013
20753013
20763013
ROGER D. MADDUX
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
···
···
ccc
···
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ddd
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
FINITE INTEGRAL RELATION ALGEBRAS
20773013
20783013
20793013
20803013
20813013
20823013
20833013
20843013
20853013
20863013
20873013
20883013
20893013
20903013
20913013
20923013
20933013
20943013
20953013
20963013
20973013
20983013
20993013
21003013
21013013
21023013
21033013
21043013
21053013
21063013
21073013
21083013
21093013
21103013
21113013
21123013
21133013
21143013
21153013
21163013
21173013
21183013
21193013
21203013
21213013
21223013
21233013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
bbb
···
bbb
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
ccc
···
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
ccc
···
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
···
···
···
···
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
111
daa
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
112
21243013
21253013
21263013
21273013
21283013
21293013
21303013
21313013
21323013
21333013
21343013
21353013
21363013
21373013
21383013
21393013
21403013
21413013
21423013
21433013
21443013
21453013
21463013
21473013
21483013
21493013
21503013
21513013
21523013
21533013
21543013
21553013
21563013
21573013
21583013
21593013
21603013
21613013
21623013
21633013
21643013
21653013
21663013
21673013
21683013
21693013
21703013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
ccc
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ddd
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
···
···
ddd
···
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
acc
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd dbb
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
··· ···
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
21713013
21723013
21733013
21743013
21753013
21763013
21773013
21783013
21793013
21803013
21813013
21823013
21833013
21843013
21853013
21863013
21873013
21883013
21893013
21903013
21913013
21923013
21933013
21943013
21953013
21963013
21973013
21983013
21993013
22003013
22013013
22023013
22033013
22043013
22053013
22063013
22073013
22083013
22093013
22103013
22113013
22123013
22133013
22143013
22153013
22163013
22173013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
bbb
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
113
daa
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc cbb
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bcc · · ·
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
114
22183013
22193013
22203013
22213013
22223013
22233013
22243013
22253013
22263013
22273013
22283013
22293013
22303013
22313013
22323013
22333013
22343013
22353013
22363013
22373013
22383013
22393013
22403013
22413013
22423013
22433013
22443013
22453013
22463013
22473013
22483013
22493013
22503013
22513013
22523013
22533013
22543013
22553013
22563013
22573013
22583013
22593013
22603013
22613013
22623013
22633013
22643013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
bbb
···
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ddd
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
22653013
22663013
22673013
22683013
22693013
22703013
22713013
22723013
22733013
22743013
22753013
22763013
22773013
22783013
22793013
22803013
22813013
22823013
22833013
22843013
22853013
22863013
22873013
22883013
22893013
22903013
22913013
22923013
22933013
22943013
22953013
22963013
22973013
22983013
22993013
23003013
23013013
23023013
23033013
23043013
23053013
23063013
23073013
23083013
23093013
23103013
23113013
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ddd
ddd
ddd
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
115
daa bcc cbb bdd dbb
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
116
23123013
23133013
23143013
23153013
23163013
23173013
23183013
23193013
23203013
23213013
23223013
23233013
23243013
23253013
23263013
23273013
23283013
23293013
23303013
23313013
23323013
23333013
23343013
23353013
23363013
23373013
23383013
23393013
23403013
23413013
23423013
23433013
23443013
23453013
23463013
23473013
23483013
23493013
23503013
23513013
23523013
23533013
23543013
23553013
23563013
23573013
23583013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ddd
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
abb
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa bcc cbb bdd dbb
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
daa · · · cbb bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
23593013
23603013
23613013
23623013
23633013
23643013
23653013
23663013
23673013
23683013
23693013
23703013
23713013
23723013
23733013
23743013
23753013
23763013
23773013
23783013
23793013
23803013
23813013
23823013
23833013
23843013
23853013
23863013
23873013
23883013
23893013
23903013
23913013
23923013
23933013
23943013
23953013
23963013
23973013
23983013
23993013
24003013
24013013
24023013
24033013
24043013
24053013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
bbb
···
bbb
bbb
bbb
···
···
bbb
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
ddd
ddd
ddd
···
···
···
abb
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
117
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
118
24063013
24073013
24083013
24093013
24103013
24113013
24123013
24133013
24143013
24153013
24163013
24173013
24183013
24193013
24203013
24213013
24223013
24233013
24243013
24253013
24263013
24273013
24283013
24293013
24303013
24313013
24323013
24333013
24343013
24353013
24363013
24373013
24383013
24393013
24403013
24413013
24423013
24433013
24443013
24453013
24463013
24473013
24483013
24493013
24503013
24513013
24523013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
ccc
ccc
ccc
ddd
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
acc
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
24533013
24543013
24553013
24563013
24573013
24583013
24593013
24603013
24613013
24623013
24633013
24643013
24653013
24663013
24673013
24683013
24693013
24703013
24713013
24723013
24733013
24743013
24753013
24763013
24773013
24783013
24793013
24803013
24813013
24823013
24833013
24843013
24853013
24863013
24873013
24883013
24893013
24903013
24913013
24923013
24933013
24943013
24953013
24963013
24973013
24983013
24993013
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
···
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ddd
···
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
119
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
120
25003013
25013013
25023013
25033013
25043013
25053013
25063013
25073013
25083013
25093013
25103013
25113013
25123013
25133013
25143013
25153013
25163013
25173013
25183013
25193013
25203013
25213013
25223013
25233013
25243013
25253013
25263013
25273013
25283013
25293013
25303013
25313013
25323013
25333013
25343013
25353013
25363013
25373013
25383013
25393013
25403013
25413013
25423013
25433013
25443013
25453013
25463013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
bbb
bbb
···
···
bbb
bbb
···
bbb
···
···
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
bbb
···
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
acc
acc
acc
acc
acc
acc
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb cdd
··· ···
··· ···
··· ···
··· ···
··· ···
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
25473013
25483013
25493013
25503013
25513013
25523013
25533013
25543013
25553013
25563013
25573013
25583013
25593013
25603013
25613013
25623013
25633013
25643013
25653013
25663013
25673013
25683013
25693013
25703013
25713013
25723013
25733013
25743013
25753013
25763013
25773013
25783013
25793013
25803013
25813013
25823013
25833013
25843013
25853013
25863013
25873013
25883013
25893013
25903013
25913013
25923013
25933013
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
···
···
bbb
···
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
bbb
···
···
bbb
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
121
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb cdd
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dbb · · ·
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
122
25943013
25953013
25963013
25973013
25983013
25993013
26003013
26013013
26023013
26033013
26043013
26053013
26063013
26073013
26083013
26093013
26103013
26113013
26123013
26133013
26143013
26153013
26163013
26173013
26183013
26193013
26203013
26213013
26223013
26233013
26243013
26253013
26263013
26273013
26283013
26293013
26303013
26313013
26323013
26333013
26343013
26353013
26363013
26373013
26383013
26393013
26403013
ROGER D. MADDUX
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
bbb
bbb
bbb
···
bbb
···
bbb
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
ccc
ccc
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
···
ccc
···
ccc
···
ccc
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
ccc
···
···
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ddd
ddd
ddd
···
···
···
···
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
···
···
ddd
ddd
···
···
ddd
ddd
···
ddd
···
···
ddd
ddd
···
···
···
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
baa
baa
baa
baa
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
···
···
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bdd
···
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
FINITE INTEGRAL RELATION ALGEBRAS
26413013
26423013
26433013
26443013
26453013
26463013
26473013
26483013
26493013
26503013
26513013
26523013
26533013
26543013
26553013
26563013
26573013
26583013
26593013
26603013
26613013
26623013
26633013
26643013
26653013
26663013
26673013
26683013
26693013
26703013
26713013
26723013
26733013
26743013
26753013
26763013
26773013
26783013
26793013
26803013
26813013
26823013
26833013
26843013
26853013
26863013
26873013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
ddd
···
···
ddd
ddd
ddd
ddd
···
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
baa
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa add daa bcc cbb
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
· · · · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
caa · · · daa bcc · · ·
123
bdd dbb cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
bdd · · · cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
124
26883013
26893013
26903013
26913013
26923013
26933013
26943013
26953013
26963013
26973013
26983013
26993013
27003013
27013013
27023013
27033013
27043013
27053013
27063013
27073013
27083013
27093013
27103013
27113013
27123013
27133013
27143013
27153013
27163013
27173013
27183013
27193013
27203013
27213013
27223013
27233013
27243013
27253013
27263013
27273013
27283013
27293013
27303013
27313013
27323013
27333013
27343013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
ccc
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc cbb bdd dbb cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
bcc · · · bdd · · · cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
FINITE INTEGRAL RELATION ALGEBRAS
27353013
27363013
27373013
27383013
27393013
27403013
27413013
27423013
27433013
27443013
27453013
27463013
27473013
27483013
27493013
27503013
27513013
27523013
27533013
27543013
27553013
27563013
27573013
27583013
27593013
27603013
27613013
27623013
27633013
27643013
27653013
27663013
27673013
27683013
27693013
27703013
27713013
27723013
27733013
27743013
27753013
27763013
27773013
27783013
27793013
27803013
27813013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
aaa
···
aaa
aaa
aaa
bbb
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
ccc
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
···
···
···
ccc
ddd
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
125
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
126
27823013
27833013
27843013
27853013
27863013
27873013
27883013
27893013
27903013
27913013
27923013
27933013
27943013
27953013
27963013
27973013
27983013
27993013
28003013
28013013
28023013
28033013
28043013
28053013
28063013
28073013
28083013
28093013
28103013
28113013
28123013
28133013
28143013
28153013
28163013
28173013
28183013
28193013
28203013
28213013
28223013
28233013
28243013
28253013
28263013
28273013
28283013
ROGER D. MADDUX
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
···
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
···
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
28293013
28303013
28313013
28323013
28333013
28343013
28353013
28363013
28373013
28383013
28393013
28403013
28413013
28423013
28433013
28443013
28453013
28463013
28473013
28483013
28493013
28503013
28513013
28523013
28533013
28543013
28553013
28563013
28573013
28583013
28593013
28603013
28613013
28623013
28633013
28643013
28653013
28663013
28673013
28683013
28693013
28703013
28713013
28723013
28733013
28743013
28753013
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
···
ccc
···
···
···
ccc
ccc
···
···
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
ddd
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
127
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd dbb
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
bdd · · ·
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
128
28763013
28773013
28783013
28793013
28803013
28813013
28823013
28833013
28843013
28853013
28863013
28873013
28883013
28893013
28903013
28913013
28923013
28933013
28943013
28953013
28963013
28973013
28983013
28993013
29003013
29013013
29023013
29033013
29043013
29053013
29063013
29073013
29083013
29093013
29103013
29113013
29123013
29133013
29143013
29153013
29163013
29173013
29183013
29193013
29203013
29213013
29223013
ROGER D. MADDUX
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
bbb
···
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
bbb
bbb
ccc
···
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
···
···
···
···
···
···
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
add
add
···
···
···
···
···
···
···
···
···
···
···
···
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
bdd
bdd
bdd
bdd
bdd
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dbb
···
···
···
···
···
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
29233013
29243013
29253013
29263013
29273013
29283013
29293013
29303013
29313013
29323013
29333013
29343013
29353013
29363013
29373013
29383013
29393013
29403013
29413013
29423013
29433013
29443013
29453013
29463013
29473013
29483013
29493013
29503013
29513013
29523013
29533013
29543013
29553013
29563013
29573013
29583013
29593013
29603013
29613013
29623013
29633013
29643013
29653013
29663013
29673013
29683013
29693013
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
129
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb bdd
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
cbb · · ·
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
acd bcd
130
29703013
29713013
29723013
29733013
29743013
29753013
29763013
29773013
29783013
29793013
29803013
29813013
29823013
29833013
29843013
29853013
29863013
29873013
29883013
29893013
29903013
29913013
29923013
29933013
29943013
29953013
29963013
29973013
29983013
29993013
30003013
30013013
30023013
30033013
30043013
30053013
30063013
30073013
30083013
30093013
30103013
30113013
30123013
30133013
ROGER D. MADDUX
aaa
aaa
···
aaa
aaa
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
···
aaa
aaa
···
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
···
aaa
aaa
aaa
aaa
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
···
···
bbb
bbb
bbb
bbb
bbb
bbb
···
···
bbb
bbb
···
bbb
bbb
bbb
bbb
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
···
···
bbb
bbb
bbb
ccc
ccc
ccc
ccc
ccc
ccc
···
···
···
···
ccc
ccc
ccc
ccc
···
···
ccc
ccc
···
···
···
···
ccc
ccc
ccc
···
···
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ccc
···
···
···
ccc
ccc
ddd
ddd
···
···
···
ddd
···
···
···
···
···
···
···
···
ddd
ddd
ddd
ddd
···
···
···
···
···
···
···
ddd
ddd
ddd
···
···
···
···
···
···
ddd
ddd
ddd
ddd
ddd
ddd
···
···
···
···
ddd
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
abb
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
···
···
···
···
···
···
···
···
···
···
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
baa
acc
acc
···
···
···
···
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
acc
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
caa
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
add
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
daa
bcc
bcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
bcc
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
cbb
bdd
···
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
bdd
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
dbb
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
cdd
dcc
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
···
dcc
dcc
dcc
dcc
dcc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abc
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
abd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
acd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
bcd
FINITE INTEGRAL RELATION ALGEBRAS
131
18. Failures of (J), (L), (M) among 11316 –13161316 and 13013 –30133013
alg.
361316
401316
671316
711316
761316
791316
881316
931316
961316
981316
1001316
1041316
1141316
1281316
1331316
1361316
1381316
1401316
1441316
1541316
1621316
1641316
1671316
1761316
1801316
1841316
1861316
1991316
2011316
2031316
2051316
2071316
2091316
2111316
2131316
2151316
2171316
2191316
2221316
2241316
2291316
2341316
2381316
2411316
2431316
(J)
arr̆r̆raa
arr̆r̆raa
arr̆r̆raa
arr̆r̆raa
aabrr̆bb
aabrr̆bb
(L)
raaarr̆r̆
raaarr̆r̆
raaarr̆r̆
raaar̆rr
raaar̆rr
raaar̆r̆a
raaar̆r̆a
aarrrrr
raaar̆r̆r̆
raaar̆r̆r̆
raaarr̆a
raaarr̆a
aarrrr̆r
raaar̆rr
raaar̆rr
raaar̆r̆a
raaar̆r̆a
aarrrrr
aabbbrr
abbrraa
aabbbrr
raaar̆r̆r̆
raaar̆r̆r̆
raaarr̆a
raaarr̆a
aarrrr̆r
aabbbrr
aabbbrr
(M)
arr̆aaaa
arr̆aaaa
arr̆aaaa
arr̆aaaa
aarbbbr
aarbbbr
rar̆r̆r̆r̆r̆
aaarrr̆r̆
rr̆r̆aaar
rr̆r̆aaar
arr̆aaaa
arr̆aaaa
aarr̆r̆r̆a
rar̆r̆r̆r̆r̆
aaarrr̆r̆
rr̆r̆aaar
rr̆r̆aaar
arr̆aaaa
arr̆aaaa
aarr̆r̆r̆a
aabrrab
aabrrab
aarbbbr
rar̆r̆r̆r̆r̆
abbrr̆br̆
rar̆r̆r̆r̆r̆
abbrr̆br̆
aabbbrr
aabbbrr
aabbbrr
aabbbrr
aabrrbb
aabrr̆r̆b
aabrrbb
aabrr̆r̆b
aabarbr
aarbbrr
aabrrbb
aabrrbb
aabrrbb
abr̆rbbb
abbrr̆r̆a
aabr̆rbb
aaabr̆rr̆
aabr̆rbb
aabbbrr
aabbbrr
rar̆bbbr̆
rar̆bbbr̆
aarar̆bb
rar̆r̆br̆r̆
aaabr̆rb
abbbr̆rb
aabrrba
aabrrba
aabrrba
aabrrba
aarbbbr
bbraaar
aarbbbr
bbraaar
aabrrbr
aabrrbr
aarbbbr
aabrrr̆b
aarbbbr
arr̆bbbb
arr̆aaaa
rabbbaa
aaabr̆br̆
abbrr̆rr̆
alg.
381316
421316
691316
731316
771316
801316
891316
951316
971316
991316
1021316
1061316
1161316
1291316
1351316
1371316
1391316
1421316
1461316
1561316
1631316
1661316
1681316
1771316
1831316
1851316
1891316
2001316
2021316
2041316
2061316
2081316
2101316
2121316
2141316
2161316
2181316
2211316
2231316
2251316
2301316
2361316
2391316
2421316
2441316
(J)
arr̆r̆raa
arr̆r̆raa
arr̆r̆raa
arr̆r̆raa
aabrr̆bb
aabrr̆bb
raaar̆rr
raaar̆rr
raaar̆r̆a
raaar̆r̆a
aarrrrr
raaar̆rr
raaar̆rr
raaar̆r̆a
raaar̆r̆a
aarrrrr
aabbbrr
aabbbrr
abbrraa
(L)
raaarr̆r̆
raaarr̆r̆
rbbbrr̆r̆
raaarr̆a
raaarr̆a
aarrrr̆r
raaarr̆a
raaarr̆a
aarrrr̆r
aabbbrr
aabbbrr
abbrr̆br̆
aarrrrr
aabbbrr
aabbbrr
aabbbrr
aabbbrr
aabrrbb
aabrr̆r̆b
aabrrbb
aabrr̆r̆b
aabrrbb
aabrrbb
aabrrbb
aarbbrr
aabrrbb
barr̆abb
aabrr̆r̆a
aabr̆rbb
aaabr̆rr̆
aabr̆rbb
aarrrrr̆
aabbbrr
aabbbrr
rar̆bbbr̆
rar̆bbbr̆
rar̆r̆br̆r̆
rar̆r̆br̆r̆
(M)
arr̆aaaa
arr̆aaaa
arr̆aaaa
arr̆aaaa
aarbbbr
aarbbbr
rar̆r̆r̆r̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
arr̆aaaa
arr̆aaaa
aarr̆r̆r̆a
rar̆r̆r̆r̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
arr̆aaaa
arr̆aaaa
aarr̆r̆r̆a
aarbbbr
aabrrab
aabrrab
rar̆r̆r̆r̆r̆
rar̆r̆r̆r̆r̆
rar̆r̆r̆r̆r̆
rarrraa
aarbbbr̆
bbbrrr̆r̆
aarbbbr̆
bbbrrr̆r̆
aarbbbr
brrar̆br
aarbbbr
brrar̆br
aabrrbr
aarbbbr
aabrrr̆b
aabrrr̆b
aarbbbr
abbbr̆rb
aaabr̆rr
abbbr̆rb
aaabr̆r̆r̆
abbrr̆rr̆
132
alg.
2451316
2471316
2491316
2511316
2531316
2551316
2571316
2591316
2621316
2641316
2661316
2681316
2701316
2721316
2741316
2781316
2801316
2821316
2841316
2861316
2881316
2901316
2921316
2941316
2961316
2981316
3001316
3021316
3041316
3061316
3081316
3101316
3121316
3141316
3161316
3181316
3201316
3221316
3241316
3261316
3281316
3301316
3391316
3411316
3431316
3451316
3481316
ROGER D. MADDUX
(J)
abbrrrr̆
abbbr̆ab
aabr̆rbb
abbrr̆r̆a
abr̆rbrr̆
abr̆rbrr̆
baaabr̆a
baaabr̆a
aaabr̆rr̆
aaabr̆rr̆
aabr̆rbb
abr̆rbrr̆
abbbr̆ab
abr̆rrab
aabr̆rbb
abbbr̆ar
abbbr̆ar
abbbr̆ar
abbbr̆ar
aabbbbr̆
raabr̆rr
aabbbbr̆
aabbbr̆r̆
abbbr̆ar
abbbr̆ar
abbbr̆ar
abbbr̆ar
aabbbbr̆
rr̆ar̆bbr̆
aabbbbr̆
aabbbr̆r̆
rabbr̆r̆b
abr̆rbbb
rabbr̆r̆b
abr̆rbbb
(L)
abr̆rbrr
abbbr̆rb
abbbr̆rb
abr̆rbrr
abbbr̆rr
baaabr̆a
abbbr̆rr
baaabr̆a
aaabr̆rb
aaabr̆rr
abbbr̆rr
abbbr̆rr
rabar̆br
abbbr̆rr
aaabr̆rb
rabar̆br̆
aaabr̆rb
rabar̆br̆
aabbbbr̆
aabbbbr̆
abbbr̆rb
abr̆rbrr̆
abbbr̆rb
abr̆rbrr̆
aabbbbr̆
abr̆rbrr̆
aabbbbr̆
abr̆rbrr̆
rbbbrr̆b
rbbbrr̆b
(M)
abbrr̆rr̆
aarbbab
babrrar
babrrar
aabbbar
aarrrab
aabbbar
abbr̆aar
aaabr̆br̆
aaabr̆r̆r̆
abr̆barr
abr̆barr
aarbbab
aar̆br̆r̆b
barbbr̆r̆
aaabr̆br̆
aaraaab
aaabr̆br̆
aaraaab
aarrbbr̆
abbrrr̆r̆
aarrbbr̆
abbrrr̆r̆
aar̆bbbr
abr̆r̆r̆rb
aar̆bbbr
bbbarr̆a
baarbbr̆
bbbrrr̆r̆
baarbbr̆
barabr̆r̆
arr̆bbbb
arr̆bbbb
arr̆bbbb
arr̆bbbb
abbr̆r̆rr
abbr̆r̆rr
rabr̆r̆r̆b
rabr̆r̆r̆b
babr̆aar
babr̆aar
rabbbar
rabbbar
rbbrabb
rabarbb
rabarbb
baraabb
brr̆aara
baraabb
abr̆baar
abr̆baar
arr̆abbb
bbbr̆aar
arr̆bbbb
alg.
2461316
2481316
2501316
2521316
2541316
2561316
2581316
2611316
2631316
2651316
2671316
2691316
2711316
2731316
2771316
2791316
2811316
2831316
2851316
2871316
2891316
2911316
2931316
2951316
2971316
2991316
3011316
3031316
3051316
3071316
3091316
3111316
3131316
3151316
3171316
3191316
3211316
3231316
3251316
3271316
3291316
3311316
3401316
3421316
3441316
3471316
3491316
(J)
abbrrrr̆
abbbr̆r̆a
aabr̆rbb
abr̆r̆rrb
abr̆rbrr̆
abr̆rbrr̆
baar̆rbb
abbbr̆ab
abr̆rbrr̆
aabr̆rbb
abr̆rbrr̆
abbbr̆ab
abr̆rrab
aabr̆rbb
abbbr̆ar
abbbr̆ar
abbbr̆ar
abbbr̆ar
aabbbbr̆
raabr̆rr
aabbbbr̆
aabbbr̆r̆
abbbr̆ar
abbbr̆ar
abbbr̆ar
abbbr̆ar
aabbbbr̆
rr̆ar̆bbr̆
aabbbbr̆
aabbbr̆r̆
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
aabbr̆r̆a
babarar̆
babarar̆
babarar̆
babarar̆
rbbrabb
(L)
abr̆rbrr
abr̆rbrr
abbbr̆rb
abr̆rbrr
abbbr̆rr
barr̆ar̆r
abbbr̆rr
abbbr̆rr
raarbr̆r̆
abbbr̆rr
abbbr̆rr
rabar̆br
abbbr̆rr
abbbr̆rb
babarrr
abbbr̆rb
babarrr
aabbbbr̆
aabbbbr̆
abbbr̆rb
abr̆rbrr̆
abbbr̆rb
abr̆rbrr̆
aabbbbr̆
abr̆rbrr̆
aabbbbr̆
abr̆rbrr̆
baaarr̆a
baaarr̆a
baaarr̆a
baaarr̆a
baaabr̆a
baaabr̆a
baaabr̆a
baaabr̆a
raaar̆br̆
raaar̆br̆
raaar̆br̆
raaar̆br̆
(M)
abbrr̆rr̆
aarbr̆br
barbbr̆r̆
barrbr̆r̆
aaar̆r̆rr
aaar̆r̆rr
barbbr̆r̆
aarbbab
aarrrrb
abr̆barr
abr̆barr
aarbbab
aar̆br̆r̆b
barbbr̆r̆
aarrbbr̆
aar̆r̆r̆rb
aarrbbr̆
abbarr̆a
aarrbbr̆
abbrrr̆r̆
aarrbbr̆
abbrrr̆r̆
aar̆bbbr
abr̆baar
aar̆bbbr
barrbar
baarbbr̆
bbbrrr̆r̆
baarbbr̆
barabr̆r̆
abr̆aaaa
abr̆aaaa
abr̆aaaa
abr̆aaaa
abbr̆aar
abbr̆aar
abbr̆aar
abbr̆aar
abr̆baar
abr̆baar
ar̆raaaa
ar̆raaaa
brr̆aabb
brr̆ar̆ra
brr̆aabb
arr̆bbbb
abr̆bbaa
FINITE INTEGRAL RELATION ALGEBRAS
alg.
3501316
3521316
3541316
3641316
3681316
3721316
3761316
3831316
3891316
3911316
3971316
4101316
4121316
4221316
4261316
4281316
4301316
4331316
4371316
4471316
4491316
4511316
4691316
4711316
4731316
4751316
4771316
4791316
4811316
4831316
4851316
4871316
4891316
4911316
4931316
4951316
4971316
4991316
5021316
5041316
5071316
5101316
5141316
5181316
5221316
5261316
5281316
(J)
(L)
rabbbbr̆
rabbbbr̆
aabbbbr̆
aabbbbr̆
aarbbr̆a
aarbbr̆a
aarbbr̆a
brrr̆rrb
abbbr̆rb
abbbr̆rb
aabbbbr̆
aabbbbr̆
abbrr̆ba
brr̆r̆raa
arr̆r̆raa
raabrrr
raaarr̆r̆
raabrr̆r̆
raaarrr
raaarr̆r̆
aarbr̆br
aarbr̆br
babbarr̆
aarr̆abb
babrr̆rr
babrr̆rr
babrr̆rr
babrr̆rr
abbbrar
aarr̆abb
babbar̆r
aarr̆abb
babr̆rr̆r̆
babr̆rr̆r̆
babr̆rr̆r̆
babr̆rr̆r̆
abbbrbr
abbbrbr
aarbbbr̆
aarbbbr̆
aarbbbr̆
aarbbbr̆
abbbrbr
aabbbrb
aabbbrb
aabbbrb
abbbrbr̆
aabbbrb
aabbbrb
aabbbrb
babbbra
babbbr̆a
(M)
arr̆bbbb
arr̆bbbb
arr̆bbbb
barbbbb
barbbbb
baarbbr̆
baarbbr̆
aarr̆rab
bararr̆a
bararr̆a
rabr̆r̆r̆r̆
aaraaab
aaraaab
arr̆babb
arr̆aaaa
arr̆babb
arr̆aaaa
arr̆aaaa
babbrbb
aabrrar̆
barbbrr
abrbar̆r
abbbbar
barbbrr̆
abbbbar
barr̆r̆rb
barr̆r̆rr̆
barr̆r̆rb
babbr̆r̆r
abbbbar
barbbr̆r
abbbbar
barr̆r̆rb
barr̆r̆rb
abbbrbr̆
abbbrbr̆
babbrbb
aarbbar
babbrbb
babbrbb
babbrbr
babbrbr
alg.
3511316
3531316
3631316
3671316
3711316
3751316
3821316
3881316
3901316
3961316
3981316
4111316
4131316
4251316
4271316
4291316
4311316
4351316
4461316
4481316
4501316
4681316
4701316
4721316
4741316
4761316
4781316
4801316
4821316
4841316
4861316
4881316
4901316
4921316
4941316
4961316
4981316
5001316
5031316
5061316
5081316
5111316
5161316
5201316
5241316
5271316
5291316
133
(J)
(L)
rabbbbr̆
rabbbbr̆
aabbbbr̆
aabbbbr̆
aarbbr̆a
aarbbr̆a
aarbbr̆a
abbrr̆br̆
abbbr̆rb
abbbr̆rb
aabbbbr̆
aabbbbr̆
raaabr̆a
raaabr̆a
arr̆r̆raa
brr̆r̆raa
raabrr̆r̆
raaarrr
raaarr̆r̆
aarbr̆br
aarbr̆br
abbbrbr
aarr̆abb
aabbbrb
abbbrbr
aabbbrb
abbbrbr
abbbrar
aarr̆abb
abbbrbr
aarr̆abb
aabbbrb
abbbrbr
aabbbrb
abbbrbr
abbbrbr
aarbbbr̆
aarbbbr̆
abbbrbr̆
abbbrbr̆
aabbbrb
abbbrbr̆
aabbbrb
abbbrbr̆
aarbbbr̆
aarbbbr̆
abbbrbr̆
abbbrbr̆
aabbbrb
abbbrbr̆
aabbbrb
abbbrbr̆
abbbrbr̆
abbbrbr
abbbrbr
abbbrbr̆
abbbrbr̆
abbbrbr
abbbrbr
abbbrbr
abbbrbr̆
abbbrbr̆
abbbrbr̆
(M)
arr̆bbbb
abr̆bbaa
barbbbb
barbbbb
baarbbr̆
baarbbr̆
aarbr̆r̆b
aarr̆r̆r̆a
aarr̆r̆r̆a
rabr̆r̆r̆r̆
rabr̆r̆r̆r̆
aaraaab
aaraaab
arr̆aaaa
arr̆babb
arr̆babb
arr̆aaaa
arr̆aaaa
babbrbb
babbrbb
aabrrar
aarbbar̆
aarbbar̆
barbbar̆
abbbbar
aabbbra
aarr̆br̆a
aabbbra
rabrrab
aarr̆br̆a
aarr̆br̆a
arr̆aaaa
abbbbar
aabbbr̆a
aarr̆br̆a
aabbbr̆a
rabrrab
babbrbb
aarbbar
babbrbb
barrrrr
barrrrr
134
alg.
5301316
5321316
5361316
5381316
5401316
5421316
5441316
5461316
5481316
5501316
5521316
5541316
5561316
5591316
5621316
5651316
5681316
5701316
5721316
5741316
5761316
5781316
5801316
5821316
5861316
5881316
5901316
5921316
5941316
5991316
6031316
6051316
6071316
6111316
6151316
6191316
6271316
6291316
6321316
6371316
6431316
6471316
6501316
6571316
6611316
6671316
6691316
ROGER D. MADDUX
(J)
aaaabbr
aaaabbr
(L)
aaaabbr
aaaabbr
abrr̆r̆r̆r
aaaabbr
abrr̆r̆r̆r
abr̆r̆rr̆r̆
aaaabbr
abr̆r̆rr̆r̆
aaaabbr
aaaabbr
barrabb
babbarr̆
aaarraa
baaarra
aaarr̆r̆a
rarbar̆r
aaarr̆r̆a
rarbar̆r
barrabb
barrabb
baaarar̆
baaarr̆a
baaarar̆
bbrrr̆rr̆
baaarar
abrr̆rbr
baaarar
baaarar̆
baaarar̆
baaarar̆
abrrr̆r̆r̆
aarbrbr
aarbrbr
abrrrr̆r̆
aarbrrr
aarbrrr
abrrr̆r̆r̆
aarrrbr
rabbrar
abrrrr̆r̆
aarbrrr
rabbrbr
abrr̆r̆r̆r̆
abrr̆r̆r̆r̆
bbrbr̆r̆b
abrr̆r̆r̆r̆
aabr̆rrr̆
raaar̆br̆
barbbr̆a
abr̆rrr̆r̆
(M)
aaaabrb
aaaabrb
barbbrr
barbbrr
abrrabr
aaaabr̆b
arrrarr
barrrrr
barr̆rrr
aaaabr̆b
barrrrr
barr̆rrr
arrbabb
abrabbr
aabaaar
abr̆r̆ar̆a
arrr̆rar
aabaaar
arrr̆rar
barrrbr
barrrrr
rabr̆rrr̆
aabaaar
aabaaar
aabaaar
barrrrr
rabr̆rrr̆
aarbbab
abrbbaa
aarrr̆ba
aarrr̆ba
abrbbaa
aarr̆r̆r̆a
barrrbb
rar̆r̆bbb
barbrbr
rrar̆arr
barrrbb
abr̆rrr̆r̆
bbrbrbr
abr̆rrr̆r̆
aar̆br̆rr̆
barrr̆r̆a
barrr̆r̆a
aarr̆r̆r̆a
aarr̆br̆a
aarr̆br̆a
alg.
5311316
5331316
5371316
5391316
5411316
5431316
5451316
5471316
5491316
5511316
5531316
5551316
5571316
5611316
5631316
5671316
5691316
5711316
5731316
5751316
5771316
5791316
5811316
5851316
5871316
5891316
5911316
5931316
5971316
6011316
6041316
6061316
6081316
6121316
6171316
6211316
6281316
6311316
6351316
6391316
6451316
6491316
6551316
6591316
6631316
6681316
6701316
(J)
aaaabbr
aaaabbr
(L)
aaaabbr
aaaabbr
abrr̆r̆r̆r
abbr̆rba
abr̆r̆rr̆r̆
abr̆r̆rr̆r̆
aaaabbr
aaaabbr
babarr̆r̆
aaaabrb
baaarra
aaarr̆r̆a
babbar̆r
aaarr̆r̆a
abbrr̆ba
barbrr̆r
aaaabrb
baaarr̆a
baaarar̆
baaarr̆a
bbrrr̆rr̆
baaarar
abrr̆rbr
baaarar
baaarar̆
baaarar̆
baaarar̆
abrrr̆r̆r̆
abrrrr̆r̆
(M)
aaaabrb
aaaabrb
barrrrr
barrrrr
arrrarr
arrrarr
babbrbr
babbrbr
aaaabr̆b
barrrrr
barr̆rrr
arrbabb
abrabbr
aaaabbr
rabbbr̆r
abr̆r̆ar̆a
arrr̆rar
aabaaar
arrr̆rar
arr̆bbbb
arr̆bbbb
barrrrr
rabr̆rrr̆
aabaaar
aabaaar
aabaaar
barrrrr
rabr̆rrr̆
aarbbab
abrbbbb
rar̆bbrb
rar̆bbrb
abrbbbb
abrbbbb
abrrr̆r̆r̆
aarrrbr
rabbrar
abrr̆r̆r̆r̆
abrr̆r̆r̆r̆
baarr̆ab
abrrrr̆r̆
aarbrrr
aabr̆rrr̆
abrr̆r̆r̆r̆
aabr̆rrr̆
baarr̆ab
aaabrbr
aaabrbr
aar̆br̆rr̆
abr̆rrr̆r̆
aar̆br̆rr̆
aarr̆r̆r̆a
aaabrbr̆
aaabrbr̆
aaabrrr
aaabrrr
abr̆rrr̆r̆
abr̆rrr̆r̆
aarr̆r̆r̆a
bbr̆ar̆ar
barbrbr
rrar̆arr
rar̆r̆bbb
aarrr̆ba
FINITE INTEGRAL RELATION ALGEBRAS
alg.
6711316
6731316
6751316
6771316
6791316
6811316
6871316
6911316
6951316
7021316
7101316
7121316
7141316
7161316
7181316
7201316
7231316
7261316
7291316
7331316
7411316
7431316
7451316
7531316
7551316
7611316
7651316
7671316
7701316
7811316
7901316
7921316
7941316
7961316
7981316
8001316
8021316
8061316
8081316
8111316
8141316
8161316
8181316
8201316
8221316
8241316
8261316
(J)
(L)
babarar
babarar
aarrrbr
aarrrbr
barrr̆r̆a
barrr̆r̆a
aarbrrr
aarrrr̆r̆
aabrbr̆b
barrr̆br
barr̆rbr̆
aaabrbr
aaabrbr
aarbrrr
aarbrrr
(M)
arraaab
arraaab
aarr̆br̆a
aarr̆br̆a
aarr̆r̆r̆a
aarr̆r̆r̆a
brr̆bbbb
brr̆bbbb
aaar̆bbr
aaar̆bbr
arrbbab
arrbbab
raar̆abr
raar̆abr
raar̆aar
aarrrbr
aarrrbr
abrrrrr̆
abrrrrr̆
aarrrbr
aarrrbr
arrrr̆r̆r̆
arrrr̆r̆r̆
abrrr̆rr̆
bbbrrbb
aabrbrr
aabbbrr
abrrbr̆b
bbbrr̆r̆b
aabrr̆r̆b
aabrr̆r̆b
arrrr̆r̆r̆
abrbr̆ar
abrbr̆ar
abrbr̆ar
aarr̆abb
abrbr̆ar
aarr̆abb
rabr̆br̆r̆
aaabrrr
aaabrrr
aarbbrr
aarbbrr
aarbbrr
aarbbrr
arr̆aaaa
brr̆bbbb
brr̆bbbb
rarrrar̆
arr̆bbbb
rabr̆r̆bb
arr̆bbbb
aarr̆r̆r̆a
aarr̆r̆r̆a
brr̆bbbb
brr̆bbbb
brr̆bbbb
babbrbb
aabaaar
barbarr
bar̆r̆br̆b
babbrbb
aabaaar
rar̆abr̆b
babbrbb
babbrbb
aabrrr̆a
aaabrbr̆
aaabrbr̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
alg.
6721316
6741316
6761316
6781316
6801316
6821316
6881316
6921316
7011316
7091316
7111316
7131316
7151316
7171316
7191316
7211316
7251316
7271316
7301316
7351316
7421316
7441316
7461316
7541316
7561316
7621316
7661316
7691316
7791316
7891316
7911316
7931316
7951316
7971316
7991316
8011316
8051316
8071316
8091316
8131316
8151316
8171316
8191316
8211316
8231316
8251316
8271316
(J)
brr̆r̆raa
raaar̆br̆
raaar̆br̆
aarrrbr
aarrrbr
barr̆rbr̆
raabaar
barbbr̆a
135
(L)
(M)
arrbabb
arrbabb
aarbrrr
aarrrr̆r̆
aabrbr̆b
aarr̆r̆r̆a
aarr̆r̆r̆a
brr̆bbbb
brr̆bbbb
aarbrrr
aarr̆br̆a
aarr̆br̆a
arrabaa
arrabaa
aarr̆br̆a
aarr̆br̆a
arr̆aaaa
brr̆bbbb
rarrrar̆
brr̆bbbb
rarrrar̆
arr̆bbbb
rabr̆r̆bb
arr̆bbbb
babarar
babarar
raar̆aar
raar̆aar
raar̆aar
aarrrbr
aarrrbr
brr̆bbbb
brr̆bbbb
brr̆bbbb
abrrr̆rr̆
bbbrrbb
aabbrr̆r
aabbbrr
abrrbr̆b
bbbrr̆r̆b
aabbrr̆r
aabbrr̆r
arrrr̆r̆r̆
abrbr̆ar
abrbr̆ar
abbbrbr
aarr̆abb
abbbrbr
aarr̆abb
rabr̆br̆r̆
aabbarr
barar̆bb
barbbrr
aarar̆bb
aarar̆bb
aarbbrr
aarbbrr
aabarrr
aabarrr
babbrbb
aabaaar
aabrrar
barr̆rbr
babbrbb
aabaaar
aabr̆rra
babbrbb
babbrbb
aabrrar
abrarbr̆
abrrabr̆
abbarrr
abbarbb
abbarr̆a
abbarbb
aabrrr̆r̆
aabrrr̆r̆
136
alg.
8281316
8301316
8321316
8341316
8361316
8381316
8401316
8421316
8441316
8461316
8481316
8501316
8521316
8541316
8561316
8581316
8601316
8651316
8681316
8711316
8731316
8771316
8811316
8851316
8891316
8931316
8971316
8991316
9011316
9031316
9051316
9071316
9091316
9111316
9131316
9151316
9171316
9191316
9211316
9231316
9251316
9271316
9291316
9311316
9331316
9371316
9411316
ROGER D. MADDUX
(J)
raaar̆rr
rabr̆br̆r̆
rabr̆br̆r̆
raaar̆rr
raaar̆rr
abrbr̆ra
abrbr̆ra
abrbr̆ra
abrbr̆ra
abrbr̆ra
abrbr̆ra
abrr̆brr̆
abrr̆brr̆
abrr̆brr̆
abrr̆brr̆
abrr̆brr̆
abrr̆brr̆
abbbrbr
bbbrrbb
abbbrbr
aabrbrr
aabrbrr
aabbbrb
aabbbrb
aabbbrb
aabbbrb
aarrbr̆b
aarrbr̆b
aarbbr̆b
aarrbr̆b
aarbbr̆b
aarrbr̆b
rar̆rr̆r̆b
raar̆ar̆r̆
aabbbrb
abbbr̆r̆b
aabbbrb
abbbr̆r̆b
aarrbr̆b
aarrbr̆b
aarbbr̆b
aarrbr̆b
aarbbr̆b
aarrbr̆b
aabrr̆r̆b
aabbbrb
aabbbrb
(L)
aaabrr̆b
aaabrr̆b
aarbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
aarar̆bb
(M)
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
abrr̆r̆br̆
abrr̆r̆br̆
abbr̆r̆rr
abbbbar
abbr̆r̆rr
abbbbar
abrr̆r̆br̆
abrr̆r̆br̆
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abrarbr̆
babarbb
abbarbb
aarrr̆ba
aarr̆r̆ba
aabrbra
abbbrbr̆
aarbrrr
aarbrrr
aabbbrb
aabbbrb
aabbbrb
aabbbrb
barbbr̆a
barbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
bar̆rarr̆
bar̆rarr̆
aabbbrb
abbbrr̆b
aabbbrb
abbbrr̆b
barbbr̆a
barbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
abrarbr̆
abr̆r̆abr
abrarbr̆
abrarbr̆
bar̆r̆br̆b
babbrbb
baar̆r̆rr
baar̆r̆rr
baar̆r̆rr
baar̆r̆rr
baar̆r̆rr
baar̆r̆rr
abrarbr̆
abr̆r̆abr
abrarbr̆
abrarbr̆
arr̆aaaa
arr̆aaaa
aabbbrb
aabbbrb
rabr̆br̆a
rabr̆br̆a
aabrbra
alg.
8291316
8311316
8331316
8351316
8371316
8391316
8411316
8431316
8451316
8471316
8491316
8511316
8531316
8551316
8571316
8591316
8611316
8671316
8691316
8721316
8751316
8791316
8831316
8871316
8911316
8951316
8981316
9001316
9021316
9041316
9061316
9081316
9101316
9121316
9141316
9161316
9181316
9201316
9221316
9241316
9261316
9281316
9301316
9321316
9351316
9391316
9431316
(J)
aabbbrb
aabbbrr
aabbarr
aabbarr
abrbr̆ra
abrbr̆ra
abbbrbr
abbbrbr
abbbrbr
abbbrbr
abrr̆brr̆
abrr̆brr̆
aabbbrb
aabbbr̆r̆
aabbbrb
aabbbr̆r̆
abrbr̆r̆r̆
abbbrbr
abbbrbr
bbbrrbb
abrr̆br̆r
baabbar
aabrbrr
abbbrrb
aabrbrr
abbbrrb
aaabr̆r̆b
aaabr̆r̆b
babrr̆r̆b
aar̆rabb
babrr̆r̆b
aar̆rabb
rar̆rr̆r̆b
raar̆ar̆r̆
rar̆br̆r̆b
rar̆rr̆r̆b
baarr̆rr
raar̆ar̆r̆
aaabr̆r̆b
aaabr̆r̆b
babrr̆r̆b
babrr̆r̆b
babrr̆r̆b
babrr̆r̆b
aabrr̆r̆b
aabrr̆r̆b
aabrr̆r̆b
(L)
aabarrr
aabarrr
aabarrr
aabarrr
abrrr̆r̆b
abr̆rbrr̆
aarar̆bb
aarar̆bb
aarbbr̆a
aarbbr̆a
aabar̆r̆r̆
aabar̆r̆r̆
aabar̆r̆r̆
aabar̆r̆r̆
aabar̆r̆r̆
aabar̆r̆r̆
abrrr̆r̆b
aarar̆bb
abbbrbr̆
abrrr̆r̆b
aarbrrr
abbbrr̆b
aarbrrr
abbbrr̆b
aaabrr̆b
aaabrr̆b
aarbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
bar̆rarr̆
bar̆rarr̆
bar̆rarr̆
bar̆rarr̆
bar̆rarr̆
bar̆rarr̆
aaabrr̆b
aaabrr̆b
aarbbr̆a
aarbbr̆a
aarbbr̆a
aarbbr̆a
abbbrr̆b
abbbrr̆b
(M)
aabbbra
aabrrr̆r̆
aabbbra
aabrrr̆r̆
abrarbr̆
abrr̆r̆br̆
abbarrr
abbarbb
abbar̆ra
abbarbb
abrr̆r̆br̆
abrr̆r̆br̆
aabbbr̆a
abbar̆ra
aabbbr̆a
abbar̆ra
abrarbr̆
abbarbb
babarbb
barbaar
barbaar
aarr̆r̆ba
aarr̆r̆ba
aaabrbr̆
aaabrbr̆
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
aaar̆r̆rr
abr̆r̆abr
abr̆r̆abr
bar̆r̆br̆b
babbrbb
bar̆r̆br̆b
babbrbb
FINITE INTEGRAL RELATION ALGEBRAS
alg.
9451316
9471316
9491316
9511316
9531316
9551316
9571316
9591316
9611316
9631316
9651316
9671316
9691316
9711316
9731316
9761316
9791316
9811316
9851316
9911316
9951316
9991316
10031316
10061316
10081316
10111316
10131316
10161316
10251316
10301316
10321316
10351316
10371316
10401316
10491316
10591316
10621316
10651316
10671316
10701316
10831316
10911316
10971316
10991316
11011316
11031316
11051316
(J)
abrrbr̆b
abrrbr̆b
aarbbr̆b
abbbrbr
aarbbr̆b
abbbrbr
abrr̆br̆r
abr̆rbr̆r
aabbbrb
abbbr̆r̆b
aabbbrb
abbbr̆r̆b
abrrbr̆b
abrrbr̆b
aarbbr̆b
bbbrr̆r̆b
abbbrbr
aarr̆rr̆r̆
aabr̆rr̆r̆
aarr̆rr̆r̆
abbbr̆r̆b
aabr̆rr̆r̆
abbbr̆r̆b
abrr̆baa
abrr̆baa
abbbrbr
aarbbr̆b
(L)
abrr̆br̆r
abrr̆br̆r
abbbrbr̆
abbbrbr̆
abbbrbr̆
abbbrbr̆
abrr̆br̆r
abrr̆br̆r
aabbbrb
abbbrr̆b
aabbbrb
abbbrr̆b
abbbrbr̆
abbbrbr̆
aar̆brrr̆
aar̆br̆rr̆
aar̆br̆rr̆
abbbrr̆b
aar̆br̆rr̆
abbbrr̆b
abbbrbr̆
abbbrbr̆
aabbbrb
abr̆rbaa
abr̆rbaa
abbbrbr
aarbbr̆b
aabbbrb
aabbbrb
aarbbr̆b
aabbbrb
abbbrbr̆
abbbrbr
aarbbr̆b
abbbrbr̆
abbbrbr̆
aabbbrb
aabbbrb
aabbbrb
aabbbrb
aaabrrr
aaabrrr
babarar̆
babarar̆
babarrr
raaar̆rr
raaar̆rr
abbbrbr̆
abbbrbr̆
(M)
abrarbr̆
ar̆raaaa
abrarbr̆
abrarbr̆
ar̆raaaa
ar̆raaaa
alg.
9461316
9481316
9501316
9521316
9541316
9561316
9581316
9601316
9621316
9641316
9661316
9681316
abrarbr̆ 9701316
bar̆r̆br̆b 9721316
abrarbr̆ 9751316
babbrbb 9771316
babbrbb 9801316
aarrr̆ba 9831316
abrrr̆r̆a 9891316
abrrr̆r̆a 9931316
9971316
abrrr̆r̆a 10011316
10051316
10071316
10091316
babbrbb 10121316
10151316
babbrbb 10211316
10291316
10311316
10331316
arr̆aaaa 10361316
arr̆aaaa 10391316
babbrbb 10451316
10581316
10611316
babbrbb 10631316
aarbr̆ra 10661316
10691316
babbrbb 10791316
10871316
10961316
aaabrbr̆ 10981316
aaabrbr̆ 11001316
abbarr̆a 11021316
abbarr̆a 11041316
abbarr̆a 11061316
137
(J)
abrrbr̆b
abrrbr̆b
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abr̆rbr̆r
abrrbr̆b
abrrbr̆b
abbbrbr
aarbbr̆b
bbbrr̆r̆b
abrr̆br̆r
aabbbrb
aabbbrb
aabbbrb
aabbbrb
raaar̆br̆
aabbbrb
aabbbrb
aabbbrb
aabbbrb
raaar̆br
aarbbr̆b
abbbrbr̆
abbbrbr
aabbbrb
raar̆aar
abbbrbr̆
aabbbrb
aarbbr̆b
abbbrbr̆
abbbrbr
aabbbrb
abbbrbr̆
aabbbrb
abbbrbr
aarbbr̆b
abbbrbr̆
abbbrbr̆
abbbrbr
aabbbrb
aabbbrb
abbbrbr̆
aabbbrb
aabbbrb
aaabrbr̆
raaar̆r̆r̆
aaabrrr
raaar̆rr
raaar̆rr
raaar̆rr
(L)
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abrr̆br̆r
abbbrbr̆
abbbrbr̆
(M)
ar̆rbrr̆b
bar̆r̆br̆b
brr̆abr̆r
babbrbb
brr̆abr̆r
babbrbb
bar̆r̆br̆b
bar̆r̆br̆b
abrarbr̆
brrbrba
babbrbb
aabr̆br̆a
aabr̆br̆a
brr̆aaaa
brr̆aaaa
babbrbb
babbrbb
arr̆aaaa
arr̆aaaa
arr̆aaaa
babbrbb
arr̆aaaa
babbrbb
babbrbb
aarbr̆ra
babbrbb
babbrbb
aaabrbr̆
rr̆r̆aaar
aaabrbr̆
aaarrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
138
alg.
11071316
11091316
11111316
11131316
11151316
11171316
11191316
11211316
11231316
11251316
11271316
11291316
11311316
11331316
11351316
11371316
11391316
11411316
11431316
11451316
11471316
11491316
11511316
11551316
11631316
11691316
11771316
11851316
11931316
11951316
11971316
11991316
12031316
12131316
12151316
12171316
12211316
12251316
12281316
12341316
12401316
12421316
12441316
12491316
12561316
12581316
12621316
ROGER D. MADDUX
(J)
raaar̆rr
raaar̆rr
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raaar̆r̆a
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
raabr̆ar̆
raabr̆ar̆
raabr̆ar̆
aarrrbr̆
aabrr̆rr
aarrrrr
aabrr̆rr
raaar̆r̆a
raaar̆r̆b
raaar̆r̆b
raaar̆r̆a
raaar̆r̆a
raaar̆ar̆
raar̆bbr
(L)
babarrr
abrrr̆r̆b
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abrrr̆r̆b
barar̆bb
babarar̆
aarbrrr
aarbrrr
aarbrrr
aarbrrr
raaarr̆a
aaabrr̆b
aaabrr̆b
raaarr̆a
raaarr̆a
arr̆aaaa
arr̆babb
arr̆babb
arr̆aaaa
arr̆aaaa
ar̆raaaa
brr̆bbbb
ar̆raaaa
ar̆raaaa
raaar̆ar̆
baarr̆br
baarr̆br
raar̆bbr
raar̆bbr
(M)
abbarr̆a
aabrrr̆r̆
aaarrr̆r̆
aaarrr̆r̆
arr̆aaaa
arr̆aaaa
arr̆aaaa
arr̆aaaa
abbar̆ra
abbar̆ra
abbar̆ra
abbar̆ra
arr̆r̆bbr
bbbr̆r̆rr
arr̆r̆bbr
bbbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
arr̆bbbb
bbbarrr
arr̆bbbb
aarbrrr
aarbrrr
arr̆bbbb
arr̆bbbb
raar̆bar
bbrrrbr̆
rbbr̆bbr
rbabbr̆b
rbbbrbr̆
brr̆bbbb
brr̆bbbb
alg.
11081316
11101316
11121316
11141316
11161316
11181316
11201316
11221316
11241316
11261316
11281316
11301316
11321316
11341316
11361316
11381316
11401316
11421316
11441316
11461316
11481316
11501316
11521316
11571316
11641316
11711316
11791316
11871316
11941316
11961316
11981316
12011316
12051316
12141316
12161316
12191316
12231316
12271316
12331316
12391316
12411316
12431316
12471316
12551316
12571316
12611316
12631316
(J)
raaar̆rr
raaar̆rr
raaar̆rr
raabr̆r̆a
raabr̆r̆a
raabr̆r̆a
raabr̆r̆a
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
raar̆br̆r̆
rbbbr̆ar̆
rbbbr̆ar̆
(L)
aaabrr̆b
aaabrr̆b
aaabrr̆b
aaabrr̆b
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
abr̆rbrr̆
rarbbbr̆
(M)
aaarrr̆r̆
aaarrr̆r̆
aabrrr̆r̆
aaarrr̆r̆
aaar̆bbr
arr̆babb
arr̆babb
arr̆babb
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
arr̆r̆bbr
bbbr̆r̆rr
arr̆r̆bbr
bbbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
abbr̆r̆rr
arr̆bbbb
arr̆bbbb
raabr̆ar̆
bbrrrbr̆
aabrr̆rr
aarrrrr
aabrr̆rr
raaar̆r̆b
raaar̆r̆a
raaar̆r̆b
raaar̆r̆a
raaar̆r̆a
raar̆bbr
babarar̆
aarbrrr
aarbrrr
aarbrrr
aaabrr̆b
raaarr̆a
aaabrr̆b
raaarr̆a
raaarr̆a
raaar̆ar̆
aarr̆rbr̆
aabr̆rr̆r̆
raar̆bar
raar̆bar
raar̆bar
aarrrbr̆
rbbr̆bbr
aabr̆rr̆r̆
aabr̆rr̆r̆
aaar̆bbr
arr̆aaaa
arr̆babb
arr̆aaaa
arr̆aaaa
aaarbbr̆
ar̆raaaa
ar̆raaaa
ar̆raaaa
aarbrrr
aarbrrr
arr̆bbbb
bbbr̆aar
arr̆bbbb
aar̆br̆rr̆
aar̆br̆rr̆
aar̆br̆rr̆
brr̆bbbb
brr̆bbbb
FINITE INTEGRAL RELATION ALGEBRAS
alg.
12651316
12691316
12771316
12971316
13051316
543013
573013
593013
713013
733013
753013
793013
813013
1043013
1063013
1093013
1133013
1163013
1183013
1233013
1253013
1273013
1323013
1343013
1453013
1533013
1863013
1883013
1913013
1953013
1983013
2003013
2053013
2073013
2093013
2143013
2163013
2273013
2353013
2483013
2503013
2523013
2573013
2633013
2713013
2733013
2813013
(J)
(L)
aarr̆rbr̆
aabr̆rr̆r̆
raaar̆ar̆
abbrr̆br̆
aabccbb
aabccbb
aacbbcc
aabddbb
aabddbb
aadbbdd
aabccbb
aadbbdd
aar̆br̆rr̆
aar̆br̆rr̆
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabddbb
aadbbdd
aabddbb
aabbbcb
aabbbcb
aadbcdd
aadbcdd
daaabad
daaabad
(M)
brr̆bbbb
aabccbc
aabccbc
aabccbc
aabddbd
aabddbd
aabddbd
aabccbc
aabddbd
babbcbb
babbcbb
aabccac
aaaacbc
aaaacbc
aaaacbc
aabbbca
abcaacc
aabbbca
abccccc
abccccc
babbcbb
babbcbb
aabccac
aaaacbc
aaaacbc
aaaacbc
aabbbca
abcaacc
aabbbca
abccccc
abccccc
aabddbd
aabddbd
aadbbbd
aadaaab
abdbbbb
aacaaab
aacaaab
aadddab
alg.
12661316
12711316
12791316
12991316
533013
553013
583013
703013
723013
743013
783013
803013
1033013
1053013
1073013
1123013
1143013
1173013
1193013
1243013
1263013
1313013
1333013
1413013
1493013
1853013
1873013
1893013
1943013
1963013
1993013
2013013
2063013
2083013
2133013
2153013
2233013
2313013
2473013
2493013
2513013
2533013
2583013
2643013
2723013
2743013
2873013
139
(J)
(L)
aarr̆rbr̆
aabr̆rr̆r̆
raaar̆ar̆
aabccbb
aacbbcc
aabccbb
aabddbb
aadbbdd
aabddbb
aabccbb
aacbbcc
aar̆br̆rr̆
aar̆br̆rr̆
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aaaaccb
aaaaccb
aaaaccb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabddbb
aacddcc
aabddbb
aacddcc
aabbbcb
aabbbcb
aadbcdd
aadbcdd
daabdbb
dabadbb
(M)
brr̆bbbb
aabccbc
aabccbc
aabccbc
aabddbd
aabddbd
aabddbd
aabccbc
aabccbc
babbcbb
babbcbb
aabccac
aaaacbc
aaaacbc
aaaacbc
aabbbca
abccccc
abccccc
aabbbca
abcaacc
babbcbb
babbcbb
aabccac
aaaacbc
aaaacbc
aaaacbc
aabbbca
abccccc
abccccc
aabbbca
abcaacc
aabddbd
aabddbd
aadbbbd
aadbccd
aadaaab
abdbbbb
aacaaab
aacaaab
abdddbb
140
alg.
3073013
3113013
3133013
3153013
3193013
3233013
3253013
3273013
3293013
3313013
3333013
3353013
3373013
3393013
3413013
3433013
3453013
3473013
3493013
3513013
3533013
3553013
3573013
3593013
3613013
3633013
3653013
3683013
3703013
3723013
3743013
3763013
3783013
3813013
3863013
3883013
3903013
3923013
3943013
4023013
4043013
4063013
4083013
4103013
4123013
4143013
4163013
ROGER D. MADDUX
(J)
cbbddad
cbbddad
cbbddbc
cbbddad
cbbddbc
aaaacbc
aaaacbc
aacddcc
aacddcc
aacddcc
aacddcc
aacbcad
aadbdac
aacbcad
abcddba
aacbcad
aacbcad
aadbdac
aadbdac
aacbcad
aacbcad
abcddba
accddab
aacbcad
aadccdd
aacbcad
accddab
aacddcc
aacddcc
aadccdd
aadccdd
aacddcc
aacddcc
accddab
caaddbd
caaddbd
caaddbd
aaaacbc
aadbdac
aaaadbd
bccddaa
aacbcad
aacbcad
aadbdac
aadbdac
(L)
(M)
abcbbbb
abcbbbb
aaabcdb
aaabcdb
abcbddd
bacbbda
abcbddd
aacbcdd
abcbddd
bacbbda
bacbbda
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
aaabcdb
aaabcdb
aaabcdb
aaabcbd
aaabcbd
aacddcd
abdacdb
aabddad
abdacdc
aacddcd
aacddcd
aadcbbd
aadcbbd
aacddcd
aacddcd
aacddcd
aacddcd
aadcccd
aadcccd
abbacda
abbacda
aacddcd
aacddcd
aadcccd
badbcad
aacddcd
aacddcd
aacddcd
aacddcd
aadcccd
aadcccd
badbcad
aacaaab
aacaaab
aacaaab
aaabcbd
aacddcd
aaabcbd
aaabcbd
aacddcd
aacddcd
aacddcd
aacddcd
alg.
3093013
3123013
3143013
3163013
3203013
3243013
3263013
3283013
3303013
3323013
3343013
3363013
3383013
3403013
3423013
3443013
3463013
3483013
3503013
3523013
3543013
3563013
3583013
3603013
3623013
3643013
3673013
3693013
3713013
3733013
3753013
3773013
3793013
3833013
3873013
3893013
3913013
3933013
4013013
4033013
4053013
4073013
4093013
4113013
4133013
4153013
4173013
(J)
cbbddbc
(L)
(M)
abcbbbb
abcbbbb
cbbddad
cbbddbc
aaabdbd
abcdbaa
abcdbdd
abcddab
abcdbdd
ccdddab
aaaacbc
aaaadbd
aaaacbc
abcdbaa
aacddcc
aacddcc
aadccdd
aadccdd
aacddcc
aacddcc
bccddab
bacdabb
aacddcc
aadccdd
aacddcc
aacbcad
aacbcad
aadccdd
aadccdd
aacbcad
aacbcad
abbddba
caaddbd
caaddbd
caaddbd
aacbcad
aaaacbc
aaaadbd
accddaa
cacddba
aacddcc
aacddcc
aadccdd
aadccdd
aaabcdb
aaabcdb
abcbddd
bacbbda
abcbddd
aaabcbd
aaabcbd
aacddcd
abdacdb
aabddad
aaabcdb
aaabcdb
aaabcdb
aaabcdb
abcbddd
abcbddd
abcbddd
abcbddd
aaabcbd
aaabcbd
aaabcbd
aaabcbd
aacddcd
aacddcd
aacddcd
aacddcd
aadcccd
aadcccd
badbcbd
babbdbb
aacddcd
aacddcd
aadcccd
aacddcd
aacddcd
aacddcd
aacddcd
aadcccd
aadcccd
badbcad
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
abcbddd
aacaaab
aacaaab
aacaaab
aacbcdd
aaabcdb
aaabcdb
aaabcdb
aacddcd
aaabcbd
aaabcbd
ccdaaad
aaabcbd
aacddcd
aacddcd
aacddcd
aacddcd
FINITE INTEGRAL RELATION ALGEBRAS
alg.
4183013
4223013
4243013
4263013
4563013
4603013
4623013
4723013
4763013
4783013
4963013
5123013
5163013
5203013
5243013
5333013
5353013
5373013
5393013
5413013
5433013
5453013
5493013
5513013
5533013
5553013
5573013
5593013
5613013
5633013
5653013
5673013
5693013
5713013
5743013
5783013
5813013
5833013
5853013
5873013
5893013
5913013
5933013
5953013
5983013
6003013
6033013
(J)
cacddaa
aacddcc
aacddcc
aadccdd
babddcd
babddcd
babddcd
babddcd
babddcd
babddcd
bacccbc
bacccbc
bccddbd
bacddbd
bccddbd
aaaaddb
aaaaddb
aaddacc
aaddacc
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcbd
abbbcbd
abbbcbd
abbbcbd
(L)
(M)
abbacda
aacddcd
aacddcd
aacddcd
aadbdcd
abddddd
abddddd
aadbdcd
abddddd
abddddd
aacbcdc
aacbcdc
aadbdcd
aaaaddb
aaaaddb
aaddbdc
aaddbdc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
abbbcbd
abbbcbd
abbbcbd
abbbcbd
babbcbb
babbcbb
aabccad
aabccad
aacbbad
aacbbad
aabddad
aaaadbd
aaaadbd
abcdacc
abcdacc
babbcdd
abbbbad
babbcdd
abbbbad
abdbadd
abbbbad
abdbadd
abbbbad
abddddd
abddddd
abddddd
abddddd
babbcbb
babbcbb
babbdcc
babbdcc
aacbbac
babbcbb
alg.
4203013
4233013
4253013
4273013
4583013
4613013
4633013
4743013
4773013
4793013
5003013
5143013
5183013
5223013
5323013
5343013
5363013
5383013
5403013
5423013
5443013
5483013
5503013
5523013
5543013
5563013
5583013
5603013
5623013
5643013
5663013
5683013
5703013
5723013
5763013
5803013
5823013
5843013
5863013
5883013
5903013
5923013
5943013
5963013
5993013
6023013
6043013
(J)
cacddaa
aacddcc
aadccdd
aadccdd
babddcd
141
(L)
(M)
abbacda
aacddcd
aacddcd
aacddcd
aadbdcd
abddddd
abddddd
babddcd
aadbdcd
abddddd
abddddd
bacccbc
bacddbd
bacddbd
bccddbd
aacbcdc
aadbdcd
aadbdcd
aaaaddb
aaaaddb
aaddbdc
aaddbdc
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
abbbcad
aabbbcb
aabbbcb
aabbbcb
abbbcbd
aabbbcb
abbbcbd
aaaaddb
aaaaddb
aadcbcc
aadcbcc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aadbbbc
aabbbcb
aabbbcb
aabbbcb
abbbcbd
aabbbcb
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
babbcbb
babbcbb
aabccac
aabccac
aacbbad
aacbbad
aabddad
aaaadbd
aaaadbd
aabccac
aabccac
aacbbac
aacbbac
aacbbad
aacbbad
aacbbac
aacbbac
aacbbad
aacbbad
aabbbda
aabbbda
aabbbda
abdaadd
aabbbda
abdaadd
babbcbb
babbcbb
aabccac
aabccac
aacbbac
babbcbb
babbcbb
aacbbac
142
alg.
6063013
6083013
6113013
6143013
6183013
6223013
6263013
6293013
6313013
6333013
6353013
6373013
6393013
6413013
6433013
6453013
6493013
6513013
6533013
6553013
6573013
6593013
6613013
6633013
6653013
6673013
6693013
6773013
6793013
6813013
6833013
6853013
6873013
6893013
6913013
6933013
6953013
6973013
6993013
7013013
7033013
7183013
7203013
7223013
7243013
7263013
7283013
ROGER D. MADDUX
(J)
abbbcbd
abbbcbd
(L)
abbbcbd
abbbcbd
(M)
aacbbac
babbcbb
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
babbdbb
babbdbc
babbdbb
aabccad
aabccad
aabccad
aabccad
aabddad
bccddca
aaaaddb
aaaaddb
aaaaddb
abbccda
abbccda
aaddacc
aaddacc
abbccda
abbccda
aaddacc
aaddacc
aaaaccb
aaaacdb
cabccdb
bbbccdd
bbbccdd
aaaabbd
aaaaddb
aaaaddb
aaaaddb
bacccda
bacccda
bacccda
bacccda
bacccda
bacccda
bacccda
bacccda
aaaaccb
aacbcdb
aaaabbd
aaaadbd
aaaadbd
aaaadbd
babbdcc
babbdcc
abcdacc
abcdacc
abdcadd
abdcadd
abcdacc
abcdacc
abddddd
abddddd
abddddd
babbdbb
babbdbc
babbdbb
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
aaaacbc
aabaadb
abccccc
babbcbb
babbcbb
aaaabdb
alg.
6073013
6103013
6123013
6163013
6203013
6243013
6283013
6303013
6323013
6343013
6363013
6383013
6403013
6423013
6443013
6483013
6503013
6523013
6543013
6563013
6583013
6603013
6623013
6643013
6663013
6683013
6763013
6783013
6803013
6823013
6843013
6863013
6883013
6903013
6923013
6943013
6963013
6983013
7003013
7023013
7173013
7193013
7213013
7233013
7253013
7273013
7293013
(J)
(L)
abbbcbd
aabbbcb
aabbbcb
aabbbcb
aabbbcb
abbbcbd
aabbbcb
aabbbcb
aabbbcb
aabbbcb
cbbddba
cbbddba
bccddca
aaaaddb
aaaaddb
aaaaddb
abbbdbc
abbccda
aaddacc
aaddacc
abbbdbc
abbccda
aaddacc
aaddacc
aaaaddb
aaaaddb
aaaaddb
abbbcbd
bacccda
abbbcbd
bacccda
abbbcbd
bacccda
abbbcbd
bacccda
abbbdbc
abbbcbd
abbbdbc
abbbcbd
abbbdbc
abbbcbd
abbbdbc
abbbcbd
aaaabbd
aaaaccb
dcddcbb
bbdccbb
bbbccdd
aaaabbd
aaaabbd
aaaabbd
aaaaccb
aaaabbd
aaaabbd
(M)
babbcbb
babbcbb
babbdbc
babbdbb
babbdbb
aabcbda
aabcbda
aabcbda
aabcbda
aabddad
aabddad
aaaadbd
aaaadbd
aaaadbd
aabbbda
aabccad
aabbbda
aabccad
aabbbda
aabccad
aabbbda
aabccad
abdaadd
abdaadd
abdaadd
babbdbc
babbdbb
babbdbb
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
babbdcc
aaaabdb
aaaacbc
dacbbdd
babbcbd
babbcbb
aaaabdb
aaaabdb
FINITE INTEGRAL RELATION ALGEBRAS
alg.
7303013
7323013
7343013
7363013
7383013
7403013
7423013
7443013
7463013
7483013
7503013
7523013
7543013
7563013
7583013
7603013
7623013
7643013
7663013
7683013
7703013
7723013
7743013
7763013
7783013
7803013
7823013
7843013
7873013
7903013
7923013
7943013
7963013
7993013
8033013
8063013
8083013
8103013
8123013
8143013
8163013
8183013
8203013
8253013
8273013
8293013
8313013
(J)
aaaabbd
aaaabbd
aaaabbd
aabbdcc
aabbdcc
aabbdcc
aabbdcc
aaccbdd
aabbadd
aaccbdd
aaccbdd
aaccbdd
aaccbdd
aabccdd
aabccdd
aabbadd
aabbadd
aabccdd
aabccdd
aabccdd
aabccdd
(L)
aaaabbd
aaaabbd
aaaabbd
babccdc
aacbcdc
aacbcdb
aacbcdb
aaccbdd
aaccbdd
aaccbdd
aaccbdd
aacbcdd
abcbddd
aacbcdd
abcbddd
babccdc
cacddbd
cacddbd
abbbccd
cacddbd
cacddbd
aadbdcd
aadbdcd
aabacad
abbbccd
abbbccd
bbcccad
baddacc
aaaabbd
aabcdad
aabcdad
aacbcbd
caaabad
abddbaa
babcccc
bbcccad
aaaabbd
aabddcc
aabacad
aabacad
badbccc
aaaabbd
caaabad
caaabad
badbbdb
bacbccc
aaaabbd
bacbccc
(M)
aaaabdb
aaaabdb
aaaabdb
aabccac
aabccad
aabccac
aabccad
aacddad
abccccc
aacddad
aacddad
bacdddd
abccccc
aacddad
aacddad
abdbbbb
abdbbbb
aacddad
aacddad
bacccdd
bacdddd
abccccc
acddddd
acddddd
abccccc
abccccc
accabdd
acddddd
acddddd
acddddd
acddddd
baacaad
baacaad
bbcccda
baccdcc
aaaabdb
baccdcc
aacaaab
aacaaab
bbbadbd
babbdbd
babbdbd
aaaabdb
bacdddd
alg.
7313013
7333013
7353013
7373013
7393013
7413013
7433013
7453013
7473013
7493013
7513013
7533013
7553013
7573013
7593013
7613013
7633013
7653013
7673013
7693013
7713013
7733013
7753013
7773013
7793013
7813013
7833013
7853013
7893013
7913013
7933013
7953013
7973013
8013013
8053013
8073013
8093013
8113013
8133013
8153013
8173013
8193013
8213013
8263013
8283013
8303013
8323013
(J)
aaaabbd
aaaabbd
aabbbdc
aabbbdc
aabbbdc
aabbbdc
aabbdcb
aabbadd
aabdbdc
aabdbdc
aabdbdc
aabdbdc
aabbdcb
aabbdcb
aabbadd
aabbadd
aabccdd
aabccdd
aabccdd
aabccdd
abccddb
aabdbdc
abbbccd
aabdbdc
abbbccd
aabdbdc
abbbccd
aabdbdc
aabdbdc
abbbccd
aabdbdc
abbbccd
abbbccd
abbbccd
babacdc
babacdc
aaaabbd
aabcdad
aabcdad
aacbcbd
caaabad
aaaabcb
bacccbc
bbcccad
bbcccad
aaaabbd
aabddcc
143
(L)
aaaabbd
aaaabbd
aabbdcb
aabbdcb
aacbcdc
aaccbdd
aacbcdc
aaccbdd
aabbdcb
aabbdcb
aabbdcb
aabbdcb
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
aabacad
bacbccc
aaaabbd
baaacda
baaacda
aacbcdc
caaabad
aacbcdc
badbccc
aaaabbd
(M)
aaaabdb
aaaabdb
aabcbda
aabcbda
aabcbda
aabcbda
aacddad
abccccc
aacddad
aacddad
abbccbd
abbccbd
aacddad
aacddad
accbcdd
acdbadd
aacddad
aacddad
bacbbdd
bacbbdd
abccccc
abbacbd
abbadcc
abbacbd
abbadcc
abbacbd
accabdd
abbacbd
abbacbd
accabdd
abbacbd
accabdd
baacaad
baacaad
abcabbc
abcabbc
aaaabbc
aaabacd
aaabacd
aacaaab
aacaaab
aabbdac
bacdddd
baccdcc
aaaabdb
bacdddd
144
alg.
8333013
8353013
8373013
8393013
8413013
8433013
8453013
8473013
8493013
8513013
8533013
8553013
8573013
8593013
8613013
8633013
8653013
8673013
8693013
8713013
8733013
8753013
8773013
8793013
8813013
8833013
8853013
8873013
8893013
8913013
8933013
8953013
8973013
8993013
9013013
9033013
9053013
9073013
9093013
9113013
9133013
9153013
9173013
9193013
9213013
9233013
9253013
ROGER D. MADDUX
(J)
aabddcc
bbdccdd
bbdccdd
bbddbcc
bbddbcc
aaaabbd
aaaabbd
aaaabbd
aaaabbd
aabddcc
aabddcc
aabddcc
aabddcc
aacbcbd
acdddcb
aacbcbd
caaabad
abcbdda
aabbadd
bacccbc
aacbcdc
abcdcdd
aacbcdc
caaabad
abcbddd
abcbddd
aacbcdc
bacccbc
aacbcdc
aacbcbd
bbdccdd
aacbcbd
bbddbcc
aabcdbc
abcbdda
aabbadd
aabbadd
dbbddcc
dbbddcc
aaaaddc
aaaaddc
aabadbc
aabadbc
aadcdcd
aadcdcd
aadcdcd
aadcdcd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
(L)
aaaabbd
aaaabbd
aaaabbd
aaaabbd
aacbcdd
abcbddd
aacbcdd
abcbddd
aaaaddc
aaaaddc
bacadcc
bacadcc
babaccc
bacadcc
babaccc
bacadcc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
(M)
baccdcc
babbdbd
babbdbd
babbdbd
babbdbd
aaaabdb
aaaabdb
aaaabdb
aaaabdb
bacdddd
baccdcc
bacdddd
baccdcc
aacaaab
aacaaab
aacaaab
aacaaab
aacddad
acdbadd
aacddad
aacddad
bacdddd
bacdddd
aacbcda
aacddab
aacbcda
aacddab
aacddad
aacddad
accbcdd
acdbadd
aacddad
aacddad
bacdddd
bacdddd
aaaadcd
aaaadcd
aabadcb
aabadcb
aadcdcd
aadcdcd
aadcdcd
aadcdcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
alg.
8343013
8363013
8383013
8403013
8423013
8443013
8463013
8483013
8503013
8523013
8543013
8563013
8583013
8603013
8623013
8643013
8663013
8683013
8703013
8723013
8743013
8763013
8783013
8803013
8823013
8843013
8863013
8883013
8903013
8923013
8943013
8963013
8983013
9003013
9023013
9043013
9063013
9083013
9103013
9123013
9143013
9163013
9183013
9203013
9223013
9243013
9263013
(J)
aabddcc
bbdccdd
bbdccdd
bbddbcc
bbddbcc
aaaabbd
aaaabbd
aaaabbd
aaaabbd
aabddcc
aabddcc
aabddcc
aabddcc
aacbcbd
acdddcb
aacbcbd
caaabad
abcbdda
aabbadd
(L)
aaaabbd
aaaabbd
aaaabbd
aaaabbd
abcdcdd
abcdcdd
caaabad
caaabad
abcbddd
abcbddd
dcdddca
aacbcbd
bbdccdd
aacbcbd
bbddbcc
aabcdbc
abcbdda
aabbadd
aabbadd
aacbcdd
abcbddd
aacbcdd
abcbddd
dbbddcc
dbbddcc
aaaaddc
aaaaddc
aaaabcd
aaaabcd
aadcdcd
aadcdcd
aadcdcd
aadcdcd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
daccddd
daccddd
bacbccc
daccddd
daccddd
daccddd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
(M)
baccdcc
bacdddd
baccdcc
bacdddd
baccdcc
aaaabdb
aaaabdb
aaaabdb
aaaabdb
bacdddd
baccdcc
bacdddd
baccdcc
aacaaab
aacaaab
aacaaab
aacaaab
aacddad
acdbadd
aacddad
aacddad
bacdddd
bacdddd
aacbcda
aacddab
aacbcda
aacddab
aacddad
aacddad
accbcdd
acdbadd
aacddad
aacddad
bacdddd
bacdddd
aaaadcd
aaaadcd
aaaabbc
aadaacd
aadcdcd
aadcdcd
aadcdcd
aadcdcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
FINITE INTEGRAL RELATION ALGEBRAS
alg.
9273013
9293013
9313013
9333013
9353013
9373013
9393013
9413013
9433013
9453013
9473013
9493013
9513013
9533013
9553013
9573013
9593013
9613013
9633013
9653013
9673013
9693013
9713013
9733013
9753013
9773013
9793013
9813013
9833013
9853013
9873013
9913013
9933013
9953013
9973013
9993013
10013013
10033013
10073013
10093013
10113013
10133013
10153013
10173013
10193013
10213013
10233013
(J)
aadbdbc
aadbdbc
aadbdbc
aadbdbc
abdcdac
abdcdac
aaddacc
aaddacc
aaddcbd
aaddcbd
aaddacc
aaddacc
abddbcc
abddbcc
aaddacc
aaddacc
aacbcbd
abccdad
(L)
aadbdcd
aadbdcd
aadbddc
aadbddc
abdcccd
abdcccd
abdcccd
abdcccd
aadbdcd
aadbdcd
aadbddc
aadbddc
abdcccd
abdcccd
abdcccd
abdcccd
aacbcdc
aadbccd
bacccbc
dacdcac
aacbcdc
aacbcbd
abbccad
aacbcbd
abbccad
aacbcbd
aacbcbd
abddbcc
aacbcbd
aacbcbd
abddbcc
abddbcc
abddbcc
abddbcc
abddbcc
abddbcc
abddbcc
abddbcc
abddbcc
aadbbcc
aadbbcc
baaccad
baaccad
baaccab
aadbdcd
cacbcdd
aadbdcd
aadbdcd
abdccdc
abdccdc
abdccdc
abdccdc
abdccdc
aadbdcd
aadbdcd
abdccdc
abdccdc
abdccdc
abdccdc
abdccdc
bacbccc
bacadcc
bacadcc
babaccc
(M)
aadbaba
aadbaba
aadbaba
aadbaba
aadbaba
aadbaba
aadbaba
aadbaba
bccacdd
bccacdd
baccdcc
baccdcc
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
accbcdd
dacbdbb
accbcdd
acddddd
accadcb
accadcb
baabdad
accadcb
accadcb
acddddd
acddddd
bccacdd
bccacdd
acddddd
acddddd
acddddd
acddddd
aadbbab
aadbbab
abcadcb
abcadcb
cabbbcc
alg.
9283013
9303013
9323013
9343013
9363013
9383013
9403013
9423013
9443013
9463013
9483013
9503013
9523013
9543013
9563013
9583013
9603013
9623013
9643013
9663013
9683013
9703013
9723013
9743013
9763013
9783013
9803013
9823013
9843013
9863013
9893013
9923013
9943013
9963013
9983013
10003013
10023013
10053013
10083013
10103013
10123013
10143013
10163013
10183013
10203013
10223013
10243013
145
(J)
aaddcbd
aaddcbd
aaddacc
aaddacc
acccdbd
acccdbd
aaddacc
aaddacc
aaddcbd
aaddcbd
aaddacc
aaddacc
acccdbd
acccdbd
aaddacc
aaddacc
aacbcbd
abccdad
(L)
aadbdcd
aadbdcd
aadbddc
aadbddc
abdcccd
abdcccd
abdcccd
abdcccd
aadbdcd
aadbdcd
aadbddc
aadbddc
abdcccd
abdcccd
abdcccd
abdcccd
aadbccd
aadbccd
bacccbc
aacbcdc
aacbcbd
abbccad
aacbcbd
abbccad
cacddbd
cacddbd
abddbcc
cacddbd
cacddbd
aadbdcd
cacddbd
cacddbd
abddbcc
cacddbd
cacddbd
aadbdcd
aadbdcd
abdccdc
aadbbcc
aadbbcc
badcbcc
badbbcd
babcccc
badbccc
cacbcdd
aadbdcd
aadbdcd
abdccdc
bacbccc
(M)
abcccbb
cabdbbc
baccdcc
baccdcc
abcccbb
acddddd
acddddd
acddddd
daaccbd
daaccbd
baccdcc
baccdcc
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
accbcdd
accbcdd
acddddd
cabdbbc
cabdbbc
dacadbb
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
aadbcac
aadbcac
abccbbc
abdbbac
cabbbcc
146
alg.
10253013
10273013
10293013
10313013
10333013
10353013
10373013
10393013
10413013
10433013
10453013
10473013
10493013
10513013
10533013
10553013
10573013
10593013
10613013
10633013
10653013
10673013
10693013
10713013
10733013
10753013
10773013
10793013
10813013
10833013
10853013
10883013
10913013
10953013
10973013
11013013
11043013
11063013
11083013
11103013
11133013
11173013
11213013
11253013
11293013
11333013
11373013
ROGER D. MADDUX
(J)
baaccad
baaccab
baaccad
aadbbcc
aadbbcc
aadbbcc
aadbbcc
aadbdbc
aadbdbc
aadbdbc
aadbdbc
abcddcc
abcddcc
abcddcc
abcddcc
abbddcc
abbddcc
abbddcc
abbddcc
abbddcc
abbddcc
abbddcc
abbddcc
aacbcbd
abbddad
aacbcbd
cbbbcad
abcbdad
abcbdad
baaccad
baaccad
bacccbc
abccddd
baaccad
baaccad
baaccad
aacbcbd
bbbccad
aacbcbd
bbbccad
aacbcbd
abccddd
aacbcbd
abcddcc
abbddcc
abbddcc
abbddcc
(L)
bacadcc
babaccc
bacadcc
abccddd
abccddd
abccddd
abccddd
abdcccd
abdcccd
abdcccd
abdcccd
abccddd
abccddd
abccddd
abccddd
abdcccd
abdcccd
abdcccd
abdcccd
aacbcdc
abcdcdd
aacbcdc
abccddd
abccddd
aacbcdc
abccddd
aacbcdc
(M)
cabddcc
baccdcc
baccdcc
aadbbab
aadbbab
aadbbab
aadbbab
aadccab
aadccab
aadccab
aadccab
aadccab
aadccab
aadccab
aadccab
aadddca
aadddca
aadddca
aadddca
cabddcc
cabddcc
baccdcc
baccdcc
abdbdda
abdbdda
bacddbb
bacddbb
baabcad
badbcad
bbccacb
cbcacdd
cbcacdd
cabcaad
cabcaad
cbcacdd
cabcabd
cabcabd
abccddd
abccddd
abdccdc
abdccdc
abccddd
abccddd
abdccdc
accadcb
accadcb
alg.
10263013
10283013
10303013
10323013
10343013
10363013
10383013
10403013
10423013
10443013
10463013
10483013
10503013
10523013
10543013
10563013
10583013
10603013
10623013
10643013
10663013
10683013
10703013
10723013
10743013
10763013
10783013
10803013
10823013
10843013
10873013
10893013
10933013
10963013
10993013
11033013
11053013
11073013
11093013
11113013
11153013
11193013
11233013
11273013
11313013
11353013
11393013
(J)
cbcccba
cbcccda
aadbbcc
aadbbcc
aadbbcc
aadbbcc
abcbdad
abcbdad
abcbdad
abcbdad
accddab
accddab
accddab
accddab
cbbddcc
cbbddcc
cbbddcc
cbbddcc
cbbddcc
cbbddcc
cbbddcc
cbbddcc
aacbcbd
abbddad
aacbcbd
bbbccad
dadbbcb
dadbbcb
abccddd
abccddd
abccddd
bacccbc
baaccad
aacbcbd
bbdccdd
aacbcbd
bbddbcc
aacbcbd
abccddd
aacbcbd
abcddcc
abbddcc
abbddcc
abbddcc
abbddcc
(L)
abcdcdd
abcdcdd
(M)
cabddcc
baccdcc
baccdcc
aadbcac
aadbcac
aadbcac
aadbcac
abcccbb
cabddcc
baccdcc
baccdcc
abcccbb
cabddcc
baccdcc
baccdcc
cabddcc
cabddcc
baccdcc
baccdcc
cabddcc
cabddcc
baccdcc
baccdcc
abdbdda
abdbdda
bbcccda
bbccacb
aacbcdc
abccddd
abccddd
aacbcdc
abccddd
abccddd
abdccdc
abdccdc
abccddd
abccddd
abdccdc
abdccdc
bbccacb
cabcaad
cabcaad
cbcacdd
cbcacdd
bacddbb
bacddbb
bacddbb
bacddbb
accadcb
accadcb
FINITE INTEGRAL RELATION ALGEBRAS
alg.
11413013
11443013
11463013
11483013
11503013
11523013
11543013
11563013
11583013
11603013
11623013
11663013
11683013
11703013
11723013
11743013
11763013
11783013
11803013
11823013
11843013
11863013
11883013
11903013
11923013
11943013
11963013
11983013
12003013
12023013
12043013
12073013
12113013
12153013
12193013
12233013
12263013
12283013
12313013
12333013
12373013
12413013
12453013
12473013
12493013
12513013
12533013
(J)
abbddcc
(L)
abdccdc
aaaabbc
aaaabbc
aaaabbc
aaaabbc
abcccbd
abcccbd
abcbdcc
abcbdcc
cacbbdb
bacbbcc
cabdacc
bacbbcc
bacbbcc
bacbbcc
cacccda
cacccda
caccadd
caccadd
caccadd
caccadd
cacbbdb
cacbbdb
cacbbdb
cacbbdb
cacbbdb
cacbbdb
aacccbc
abccccd
aacccbc
abccccd
abccccd
abccccd
aacccbc
abccccd
aacccbc
bacbdad
bbcbdac
babcccc
cbcccba
babcccc
bacbbcb
cabcacc
bacbbcb
bacbbcb
bacbbcb
cacccda
cacccda
daccddd
daccddd
cacccda
cacccda
(M)
baccccc
aaaabcb
aaaabcb
bacbbcc
bacbbcc
aacbbab
cabccbd
acdacbd
acdacbd
cabcddd
baabdcc
baabdcc
accbacc
accbacc
baabdcc
accbacc
cabccdd
cabccdd
accccad
accccad
cabccdd
cabccdd
accccad
accccad
bddbadc
cabdbbc
cabdbbc
aacbccc
abccccd
aacbccc
abccccd
abccccd
abccccd
aacbccc
abccccd
aacbccc
dacbbdb
dacbbdb
bacbccc
bacbccc
aacccda
aacccda
bacbbcc
baccccc
baccccc
abccbbc
abccbbc
cabbbcc
baccdcc
cabbbcc
alg.
11433013
11453013
11473013
11493013
11513013
11533013
11553013
11573013
11593013
11613013
11653013
11673013
11693013
11713013
11733013
11753013
11773013
11793013
11813013
11833013
11853013
11873013
11893013
11913013
11933013
11953013
11973013
11993013
12013013
12033013
12053013
12093013
12133013
12173013
12213013
12253013
12273013
12293013
12323013
12353013
12393013
12433013
12463013
12483013
12503013
12523013
12553013
147
(J)
(L)
aaaabbc
aaaabbc
aaaabbc
aaaabbc
abcccbd
abcccbd
abcbdcc
abcbdcc
abcbdca
abcbdca
abcbdca
abcbdca
abcbdca
abcbdca
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
aacbcbc
aacbcbc
abccccd
abccccd
aacbcbc
abccccd
aacccbc
abccccd
aacccbc
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
abccccd
aacbccc
aacbccc
abccccd
abccccd
aacbccc
abccccd
aacbccc
abccccd
aacbccc
abccccd
abccccd
abccccd
abccccd
abccccd
aacccbc
abccccd
abccccd
bacbdad
bacdabb
aacbccc
abccccd
abccccd
(M)
babbcbc
baccccc
aaaabcb
aaaabcb
baccccc
baccccc
aacddad
acdacbd
acdacbd
cabcddd
abdaaaa
abdaaaa
abdaaaa
abdaaaa
abdaaaa
abdaaaa
cabccad
cabccad
accccad
accccad
cabccad
cabccad
accccad
accccad
aacccba
aacccba
bacbdac
bacbdac
aacccba
bacbdac
aacccda
aacccda
bacbbcc
baccccc
baccccc
cbcccba
abdbdda
baccdcc
cabdcdd
baccdcc
baccdcc
148
alg.
12563013
12583013
12603013
12623013
12643013
12673013
12693013
12713013
12733013
12753013
12773013
12793013
12813013
12833013
12853013
12873013
12893013
12913013
12933013
12953013
12973013
12993013
13013013
13033013
13053013
13073013
13093013
13113013
13143013
13163013
13213013
13233013
13253013
13273013
13293013
13313013
13333013
13353013
13373013
13393013
13423013
13443013
13493013
13513013
13533013
13553013
13573013
ROGER D. MADDUX
(J)
(L)
baaacad
baaacad
baaacad
baaacad
cbcccba
bbcbdac
bbcbdac
dacbbdb
dacbbdb
abcccbd
baaacad
abcccbd
baaacad
baaacad
baaacad
baaacad
baaacad
bacbdad
caaabad
aacbcbd
caaabad
aacbcbd
caaabad
cabcbdb
cabcbdb
caaabad
caaabad
aacbcdc
caaabad
aacbcdc
caaabad
dbbbdca
dbbbdca
aacbcbd
dacbbdb
dacbbdb
aacbcbd
abcccbd
abcccbd
aaaadbc
aaaadbc
aaaaddc
aaaaddc
aaaaddc
aaaadbc
aaaadbc
aaaaddc
aaaaddc
aaaaddc
(M)
baccdcc
aabaaac
aabaaac
cabdcdd
baccdcc
baccdcc
acdbbbb
acdbbbb
badccdc
baccdcc
badccdc
baccdcc
aabaaac
aabaaac
aabaaac
aabaaac
badccdc
baccdcc
badccdc
baccdcc
aacaaab
aacaaab
aacaaab
aacaaab
aacaaab
aacaaab
bbccacb
bbccacb
cabdcdd
cabdcdd
aacddad
acdbbbb
aacbcda
aacddad
aacbcda
cadccbd
acdaccd
bbdccbd
acdaccd
bbdccbd
cabdcdd
cabdcdd
aaaadcb
aaaadcb
aaaadcd
aaaadcd
aaaadcd
alg.
12573013
12593013
12613013
12633013
12653013
12683013
12703013
12723013
12743013
12763013
12783013
12803013
12823013
12843013
12863013
12883013
12903013
12923013
12943013
12963013
12983013
13003013
13023013
13043013
13063013
13083013
13103013
13133013
13153013
13173013
13223013
13243013
13263013
13283013
13303013
13323013
13343013
13363013
13383013
13413013
13433013
13453013
13503013
13523013
13543013
13563013
13583013
(J)
baaacad
baaacad
babcccc
cbcccba
babcccc
(L)
baaacad
baaacad
bacbccc
bacbccc
bacdabb
bacdabb
abcccbd
baaacad
abcccbd
baaacad
baaacad
baaacad
baaacad
baaacad
bacbbaa
bacbbaa
aacbcbd
caaabad
aacbcbd
caaabad
caaabad
caaabad
caaabad
caaabad
caaabad
caaabad
bacccbc
aacbcdc
bacccbc
bacdabb
bacdabb
aacbcbd
aacbcdc
aacbcbd
abcccbd
abcccbd
bccddca
bccddca
aaaadbc aaaadbc
aaaadbc aaaadbc
aaaaddc aaaaddc
aaaaddc aaaaddc
aaaaddc aaaaddc
(M)
aabaaac
aabaaac
cabbbcc
baccdcc
cabbbcc
baccdcc
baccdcc
baccdcc
badccdc
baccdcc
badccdc
baccdcc
aabaaac
aabaaac
aabaaac
aabaaac
badccdc
baccdcc
badccdc
baccdcc
aacaaab
aacaaab
aacaaab
aacaaab
aacaaab
aacaaab
cabdcdd
cabdcdd
cabdcdd
aacddad
badccbd
aacbcda
aacddad
aacbcda
cadccbd
acdaccd
cabdcdd
acdaccd
cabdcdd
cabdcdd
aaaadcb
aaaadcb
aaaadcd
aaaadcd
aaaadcd
FINITE INTEGRAL RELATION ALGEBRAS
alg.
13593013
13613013
13633013
13653013
13673013
13693013
13733013
13753013
13773013
13793013
13813013
13833013
13853013
13873013
13893013
13913013
13933013
13953013
13973013
13993013
14013013
14033013
14053013
14073013
14093013
14113013
14133013
14153013
14173013
14193013
14213013
14233013
14253013
14273013
14293013
14313013
14333013
14353013
14373013
14393013
14433013
14463013
14483013
14503013
14523013
14543013
14583013
(J)
aaaaddc
(L)
aaaaddc
daccddd
daccddd
baaccab
baaccab
daccddd
daccddd
babaccc
babaccc
baaccab
daccddd
baaccab
daccddd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
abdcdac
abdcdac
aaddacc
aaddacc
abdcdac
abdcdac
aaddacc
aaddacc
baaccab
babaccc
daccddd
babaccc
daccddd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaddacc
aaddacc
baaccab
caccadd
aaddacc
aaddacc
bacbbda
dacddbc
bacbbda
aacdcdb
aacdcdb
babacad
bacccbc
dacddbc
dacddbc
dacddbc
daccddd
daccddd
daccddd
daccddd
daccddd
daccddd
daccddd
daccddd
aacbcdc
aacbcdc
(M)
aaaadcd
aadcdab
aadcdab
abccbbc
abdaaaa
cabbbcc
baccdcc
baccdcc
cabbbcc
cddacdd
baccdcc
baccdcc
aaaadcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
abcccbb
abdaaaa
abdaaaa
abdaaaa
abcccbb
abdaaaa
abdaaaa
abdaaaa
dabcccc
dabcccc
baccdcc
baccdcc
cadccdd
cadccdd
baccdcc
baccdcc
aaccbcb
aaccbcb
aaccbcb
aaccbcb
aacbcda
aacbcda
aacdada
cadbcdd
cadbcdd
cadbcdd
cadbcdd
badcbdb
badcbdb
alg.
13603013
13623013
13643013
13663013
13683013
13703013
13743013
13763013
13783013
13803013
13823013
13843013
13863013
13883013
13903013
13923013
13943013
13963013
13983013
14003013
14023013
14043013
14063013
14083013
14103013
14123013
14143013
14163013
14183013
14203013
14223013
14243013
14263013
14283013
14303013
14323013
14343013
14363013
14383013
14413013
14453013
14473013
14493013
14513013
14533013
14573013
14613013
149
(J)
(L)
aaaaddc aaaaddc
aaaabdb aaaabcb
aaaadbd
aaaabdb daccddd
acddcaa daccddd
babcccc bacbccc
bccddaa
babcccc
daccddd
bccddaa
daccddd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
bacbccc
daccddd
daccddd
daccddd
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaaaddc
aaddacc
aaddacc
caccadd
caccadd
aaddacc
aaddacc
daccddd
daccddd
daccddd
daccddd
aaddacc
aaddacc
caccadd
caccadd
aaddacc
aaddacc
aaaadbc
aaaadbc
aaaadbc
aaaadbc
bacccbc
babacad
aacdcdb
aacdcdb
babacad
babacad
bacccbc
daccddd
daccddd
daccddd
daccddd
(M)
aaaadcd
aaaabbc
aaddcab
aaaabbc
baccdcc
cabbbcc
baccdcc
baccdcc
cabbbcc
cddacdd
baccdcc
baccdcc
aaaadcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
aaaadcd
abcccbb
cabdbbc
baccdcc
baccdcc
abcccbb
cabdbbc
baccdcc
baccdcc
dabcccc
dabcccc
baccdcc
baccdcc
cadccdd
cadccdd
baccdcc
baccdcc
aacaabc
aacaabc
aacaabc
aacaabc
aacbcdc
aacbcdc
aacbcdc
aacdada
aacbcda
aacbcda
aacdada
aacdada
badcbdb
badcbdb
150
alg.
14623013
14703013
14783013
14803013
14823013
14843013
14863013
14883013
14903013
14923013
14943013
14963013
14983013
15003013
15023013
15043013
15103013
15123013
15343013
15363013
15383013
15403013
15423013
15443013
15463013
15483013
15503013
15523013
15543013
15583013
15603013
15623013
15663013
15683013
15703013
15723013
15743013
15763013
15783013
15803013
15823013
15843013
15863013
15883013
15903013
15923013
15943013
ROGER D. MADDUX
(J)
bacccbc
bacccbc
cacbbda
bacbbda
cacbbda
bacbbda
abbccad
abbccad
abbccad
abbccad
abbccad
abbccad
abbccad
abbccad
(L)
aacbcdc
aacbcdc
aadbcac
aadbcac
aadbcac
aadbcac
aadbcac
aadbcac
bccddad
daaabca
babcccc
bccddad
bacbccc
babcccc
cbcccba
bacbccc
bacdabb
bacdabb
(M)
abddbdb
abcbbad
acdbadd
abcbbad
bccacda
bccacda
bccacda
bccacda
cadbcdd
cadbcdd
cabdbbc
cabdbbc
cabdbbc
cabdbbc
aaacbad
baccdcc
baccdcc
baccdcc
abccbbc
baccdcc
abccbbc
baccdcc
cabbbcc
baccdcc
baccdcc
cabbbcc
baccdcc
baccdcc
baccdcc
baccdcc
caccdcb
baccdcc
caccdcb
baccdcc
abcccbb
dabcccc
baccdcc
baccdcc
abcccbb
dabcccc
baccdcc
alg.
14693013
14773013
14793013
14813013
14833013
14853013
14873013
14893013
14913013
14933013
14953013
14973013
14993013
15013013
15033013
15093013
15113013
15333013
15353013
15373013
15393013
15413013
15433013
15453013
15473013
15493013
15513013
15533013
15573013
15593013
15613013
15653013
15673013
15693013
15713013
15733013
15753013
15773013
15793013
15813013
15833013
15853013
15873013
15893013
15913013
15933013
15953013
(J)
bacccbc
cabacad
bacbbda
cabacad
bacbbda
aacdcdb
aacdcdb
abbccad
abbccad
aacdcdb
aacdcdb
abbccad
abbccad
abdcdac
abdcdac
abdcdac
abdcdac
aadbcac
aadbcac
aadbcac
aadbcac
aadbcac
aadbcac
bccddad
(L)
aacbcdc
abccccd
abccccd
abccccd
abccccd
daaabca
bacbccc
bacbccc
baaccab
baaccab
babaccc
babaccc
baaccab
baaccab
babaccc
babaccc
bbcbdac
bbcbdac
(M)
abddbca
abcbbad
abddbca
abcbbad
aacbcda
aacbcda
abddbca
abddbca
aacbcda
aacbcda
abddbca
abddbca
cabcaad
cabcaad
cabcaad
cabcaad
aaacbad
abccbbc
cabbbcc
baccdcc
cabbbcc
baccdcc
abccbbc
baccdcc
abccbbc
baccdcc
cabbbcc
baccdcc
baccdcc
cabbbcc
baccdcc
baccdcc
acdbbbb
acdbbbb
caccdcb
baccdcc
caccdcb
baccdcc
abcccbb
dabcccc
baccdcc
baccdcc
abcccbb
dabcccc
baccdcc
baccdcc
FINITE INTEGRAL RELATION ALGEBRAS
alg.
15963013
15983013
16003013
16023013
16043013
16063013
16083013
16103013
16123013
16143013
16163013
16183013
16203013
16223013
16253013
16293013
16313013
16353013
16383013
16423013
16463013
16543013
16623013
16643013
16663013
16683013
16713013
16753013
16793013
16833013
17183013
17203013
17223013
17243013
17263013
17283013
17303013
17323013
17343013
17363013
17383013
17403013
17423013
17443013
17463013
17483013
17503013
(J)
(L)
bccddad
bbbbdac
bbbbdac
bacccbc
babbdac
babbdac
babbdac
babbdac
(M)
baccdcc
dabcccc
dabcccc
baccdcc
baccdcc
dabcccc
dabcccc
baccdcc
baccdcc
aaccbcb
aaccbcb
aaccbcb
aaccbcb
aacbcdc
aacbcdc
bbdccba
bbccacb
bbccacb
bacccbc
bacccbc
aacbcdc
aacbcdc
acdbbbb
cabdcbb
acdbbbb
cabdcbb
bbbbdac
bbbbdac
abbcdcc
babbdac
abbcdcc
babbdac
bacdabb
bacdabb
bacbbda
bacbbda
cabdacc
cabdacc
aaacdaa
aaacdaa
aaacdaa
abcdddd
bbbacad
abcdddd
abcdddd
baaacad
baaacad
baaacad
aabaaac
aabaaac
aabaaac
abcdddd
abcdddd
abccccd
abccccd
cabdacc
cabdacc
abcdddd
babbadd
dabcadd
baaacad
baaacad
baaacad
baaacad
baaacad
baaacad
aabaaac
aabaaac
aabaaac
alg.
15973013
15993013
16013013
16033013
16053013
16073013
16093013
16113013
16133013
16153013
16173013
16193013
16213013
16233013
16273013
16303013
16333013
16373013
16413013
16453013
16533013
16613013
16633013
16653013
16673013
16693013
16733013
16773013
16813013
17173013
17193013
17213013
17233013
17253013
17273013
17293013
17313013
17333013
17353013
17373013
17393013
17413013
17433013
17453013
17473013
17493013
17513013
(J)
baaccab
151
(L)
baaccab
baaccab
baaccab
bccddad
bbbbdac
bbbbdac
babbdac
babbdac
babbdac
bacccbc
babbdac
aacbcdc
(M)
dabcccc
dabcccc
baccdcc
baccdcc
dabcccc
dabcccc
baccdcc
baccdcc
aaccbcb
aaccbcb
aaccbcb
aaccbcb
bbdccba
aacbcdc
bbccacb
bbccacb
bacccbc
bacccbc
daabbac
bbbbdac
daabbac
bbbbdac
abbcdcc
babbdac
abbcdcc
babbdac
aacbcdc
aacbcdc
bacdabb
cadcbab
babbacc
babbacc
aaaabcb
aaaabcb
aaaabcb
baaacda
baaacda
baaacda
bacbbda
abccccd
acdbbbb
bbcdbca
acdbbbb
bbcdbca
bbdccba
abccccd
bbdccba
aaaabcb
aaaabcb
aaaabcb
baaacda
baaacda
baaacda
abccbcb
abcdddd
abcabbc
abcabbc
abcabbc
aaaabbc
aaaabbc
aaaabbc
abcdddd
abcdddd
abcdddd
abcdddd
caccadd
baaacad
baaacad
baaacad
baaacad
baaacad
baaacad
baaacad
baaacad
aabaaac
aabaaac
aabaaac
aabaaac
152
alg.
17523013
17543013
17563013
17583013
17603013
17623013
17643013
17663013
17683013
17703013
17723013
17743013
17763013
17783013
17803013
17823013
17843013
17863013
17903013
17923013
17943013
17963013
17983013
18063013
18083013
18103013
18193013
18233013
18273013
18333013
18413013
18473013
18533013
18583013
18993013
19023013
19043013
19063013
19093013
19133013
19173013
19213013
19253013
19283013
19303013
19323013
19353013
ROGER D. MADDUX
(J)
baaacad
caccadd
dabcadd
aaaabcb
aaaacbc
dbbccaa
aaaabcb
aaaacbc
(L)
baaacad
aaaabdb
aaaabdb
cbbddba
dbbccba
cbbddba
dbdddba
bccddca
bccddca
dcdddca
baaacad
baaacad
baaacad
(M)
aabaaac
abcdddd
abcdddd
aaabadc
aabcabd
abcdddd
aaabadc
bacacda
dbbaada
abcdddd
abcdddd
abcdddd
abcdddd
dbdacdc
dbdacdc
abcdddd
abcdddd
abcdddd
baaacad
baaacad
baaacad
aabaaac
aabaaac
aabaaac
abcaaaa
abcaaaa
abcaaaa
baaddab
baaddab
caaddac
caaddac
aabbcdd
aabdcdd
aabbbdc
aabbbdc
aabbbcb
aabbbcb
aabbbdc
aabcbdc
abbbccd
babdacc
aabbdcc
cbddbaa
aabcacb
cabcacc
dabdadd
dacdadd
aabbbcb
aabbbcb
abbbccd
aacbccc
abbbccd
aabaaac
addbadd
addcadd
badbadd
aabbbca
aabbbda
babbaad
aacdcba
babbcbb
aabccda
aabcdac
dabaadc
alg.
17533013
17553013
17573013
17593013
17613013
17633013
17653013
17673013
17693013
17713013
17733013
17753013
17773013
17793013
17813013
17833013
17853013
17893013
17913013
17933013
17953013
17973013
18053013
18073013
18093013
18173013
18213013
18253013
18293013
18373013
18453013
18513013
18573013
18983013
19003013
19033013
19053013
19073013
19113013
19153013
19193013
19233013
19273013
19293013
19313013
19333013
19393013
(J)
cbbddba
(L)
(M)
abcdddd
abcdddd
aabcacb
aabcabd
aabcabd
abcaaaa
abcaaaa
abcaaaa
abcaaaa
abcdddd
abcdddd
abcdddd
abcdddd
dbdacdc
dbdacdc
dcdabdb
abcdddd
abcdddd
abcdddd
dbdacdc
dbdacdc
aabaaac
aabaaac
aabaaac
abcaaaa
abcaaaa
abcaaaa
caccadd
dabcadd
baaddab
baaddab
baaddab
baaddab
baaddab
caaddac
baaddab
caaddac
baaacad
baaacad
baaacad
baaacad
baaacad
baaacad
baaddab
baaddab
baaddab
baaddab
aabcacb
bbbcdbb
aabbbcd
aabbbdc
aabbbdc
abccddb
aabbbcd
aabbbdc
aabbbcb
aabdbcd
abddbcc
babbcbb
aabccac
bababdc
abccddb
abbbccd
aacbccc
aabbbcb
aadbdcd
bacbaad
bababcd
aacccda
aabcbda
babbcbb
aabccac
aaacacd
aabcdcd
dbcadcc
FINITE INTEGRAL RELATION ALGEBRAS
alg.
19413013
19433013
19453013
19473013
19493013
19513013
19533013
19553013
19573013
19593013
19623013
19643013
19663013
19703013
19723013
19743013
19763013
19783013
19803013
19823013
19843013
19863013
19883013
19903013
19923013
19963013
20003013
20043013
20063013
20083013
20103013
20123013
20143013
20163013
20183013
20203013
20223013
20243013
20263013
20283013
20323013
20363013
20403013
20443013
20483013
20523013
20573013
(J)
dbcdddd
dadddba
dbcdddd
aaccbdd
cadbcdd
cadbcdd
dadddca
dbcdddd
accddca
abccddd
abccddd
abccddd
abccddd
abbddcc
aadbdcb
bcccdad
bcccdad
bacccdc
baccdad
aabbbcb
babcdad
aadcdbc
cbcbdad
aadcdbc
aabbbcb
aabbbcb
aadbdcb
aadddcb
aadddcb
aadddbc
aadbdcd
aadddbc
aabbbcb
aadbdcd
aabbbcb
aadddcb
aadcdbc
aadddbc
aadcdbc
aadcdbc
aabbbcb
aabbbcb
aabbbcb
aabbbcb
abddcbc
dbcdddd
(L)
dabdadd
dacdadd
dabdadd
dacdadd
aacdcdd
aacdcdd
abccddd
abccddd
abccddd
abccddd
bacccdc
aabbbcb
aabbbcb
aabbbcb
bacccdc
aadbccd
abccddd
aabbbcb
aadbdcd
aabbbcb
abccddd
aadbccd
abccddd
aabbbcb
aabbbcb
aabbbcb
aabbbcb
abcbddc
(M)
babbcbb
aabaaac
aabccac
aacaaab
abccccc
abccccc
abccccc
abccccc
aacbdab
dabaadc
addabdd
addabdd
addabdd
addabdd
aadaaab
abcccac
babbccc
abccccc
abccccc
abccccc
abccccc
cadadbc
dacdabc
cadadbc
badadcb
badadcb
aadbbac
abcccac
babbccc
abccccc
aadddba
abccccc
aadbdca
aadddca
abccccc
abccccc
aadcdba
dacdaab
aadbdca
aadbdca
bacddbd
alg.
19423013
19443013
19463013
19483013
19503013
19523013
19543013
19563013
19583013
19603013
19633013
19653013
19683013
19713013
19733013
19753013
19773013
19793013
19813013
19833013
19853013
19873013
19893013
19913013
19943013
19983013
20023013
20053013
20073013
20093013
20113013
20133013
20153013
20173013
20193013
20213013
20233013
20253013
20273013
20303013
20343013
20383013
20423013
20463013
20503013
20563013
20583013
(J)
cbdccdd
aabbdcc
aabbdcc
abccddd
abccddd
abccddd
abccddd
dbcdddd
abccddd
abccddd
accddca
dadddba
abbddcc
dbcdddd
dbcdddd
aadbdcb
aaddacc
babdacc
bbbcdad
bacccdc
153
(L)
dabdadd
abccddd
abccddd
abccddd
abccddd
aacdcdd
abccddd
aacdcdd
dabdadd
abccddd
bacccdc
aadcdbc
bbbcdad
abddbcc
babcdad
abddbcc
aadbdcb
aadddcb
aadddcb
aadddbc
bacccdc
bacccdc
bacccdc
bacccdc
aadcdbc
aadddbc
aadcdbd
aadddbc
aadddbd
aadddbd
abccddd
abbddcc
dbcdddd
dbcdddd
aadbccd
abccddd
aadbdcd
aadbdcd
abccddd
abccddd
(M)
babbcbb
aabaaac
aabccda
aabacac
aabacac
aabcdca
aabcdca
aacbcda
cadddab
cadddab
addbadd
addbadd
dbcadcc
baddddd
baddddd
aadaaab
dabcdcc
babbdcc
abccccc
abccccc
abccccc
abccccc
babbcbb
babbcbb
dabdaac
dabdaab
dabdaab
aadbbba
abdccda
babbdcc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
babbcbb
babbcbb
aadddba
dacdaab
bacddbb
bacddbd
154
alg.
20593013
20613013
20633013
20653013
20673013
20693013
20713013
20743013
20763013
20793013
20833013
20853013
20873013
20893013
20913013
20933013
20953013
20973013
21003013
21043013
21083013
21113013
21133013
21153013
21173013
21193013
21233013
21273013
21313013
21353013
21393013
21433013
21453013
21473013
21493013
21513013
21533013
21553013
21573013
21593013
21613013
21633013
21653013
21673013
21693013
21713013
21733013
ROGER D. MADDUX
(J)
dadddba
dbcdddd
dbcdddd
abcdddd
abcdddd
abbddba
abcdddd
abbddba
dadddca
abcdddd
abbddbc
abcdddd
abcdddd
aadbbcb
aadbdcb
aaddabc
bbcdcad
bbcdcad
aadbbcb
abddcbc
babcdad
aadbdcb
aaddabc
aadbbcb
aadbbcb
aadbdcd
aadbbcb
aadbbcb
aadddbd
aadddbd
abcdddd
aaccadd
babcadd
dbdddac
accddca
accddca
dadddac
(L)
dabdadd
abdcddd
abdcddd
aabdbdd
abdcddd
aabdbdd
dacdadd
abcdcdd
abcbddc
abcdcdd
abdcddd
abcbddc
aadbcdd
aadbdcd
abcbddd
aadbdcd
aadbdcd
abcdcdd
(M)
aabaaac
aabddac
aabddad
abcaaaa
abcaaaa
dabddac
dabddac
addcadd
addcadd
addabdd
addabdd
addabdd
aadaaab
aadaaab
bbcadba
dabdacb
dabdacb
badadcb
dabdaab
dabdaab
aadbbac
abcccda
cabddcc
dabddcc
aadddba
aadbdca
dabdaac
babbcbb
babbcbb
aabccad
aacaaab
aabacac
aabacac
aabcdca
aabcdca
aacbbad
aacbcda
abcddaa
abcddaa
abcddaa
abcddaa
babbcdd
babbcdd
alg.
20603013
20623013
20643013
20663013
20683013
20703013
20733013
20753013
20773013
20813013
20843013
20863013
20883013
20903013
20923013
20943013
20963013
20983013
21023013
21063013
21103013
21123013
21143013
21163013
21183013
21213013
21253013
21293013
21333013
21373013
21413013
21443013
21463013
21483013
21503013
21523013
21543013
21563013
21583013
21603013
21623013
21643013
21663013
21683013
21703013
21723013
21743013
(J)
dadddba
dbcdddd
dbcdddd
badcbdd
badcbdd
abbddba
abbddba
abcdddd
abbddbc
abcdddd
dbcdddd
dbcdddd
dbcdddd
aadbdcb
aaddabc
aadbbcb
aadbbcb
aaddabc
babcdad
babcdad
aadbbcb
aadbdcb
aaddabc
aadddcb
aadddcb
aaddabc
aadbdcd
aadddcb
aadddbd
abbddbc
abcdddd
aaccbdd
aaccadd
babcadd
dbdddac
accddca
accddca
(L)
dabdadd
dabdadd
aabdbdd
aabdbdd
abdcddd
abcbddc
abdcddd
abddcdd
aadbdcd
abddcdd
aadbdcd
abcbddc
abddcdd
(M)
aabaaac
aabddac
aabddad
bbcadbd
addbadd
dacaadb
addabdd
addabdd
baddddd
baddddd
baddddd
aadaaab
abcccda
badadcb
badadcb
abcadbb
dabdaab
dabdaab
aadbbac
badadcb
abdccda
cabddcc
dabddcc
abcadbb
aadddca
dabdaac
babbcbb
aabccac
aabccda
aacaaab
abccccc
abccccc
abccccc
abccccc
aacbbad
aacbdab
abcddad
abcddad
cabccdd
cabdcdd
babbcdd
babbcdd
FINITE INTEGRAL RELATION ALGEBRAS
alg.
21753013
21773013
21793013
21813013
21833013
21853013
21873013
21893013
21913013
21933013
21953013
21973013
21993013
22013013
22043013
22083013
22133013
22193013
22233013
22273013
22293013
22313013
22333013
22353013
22373013
22393013
22413013
22433013
22453013
22473013
22493013
22513013
22533013
22553013
22573013
22603013
22623013
22643013
22663013
22683013
22703013
22723013
22743013
22783013
22803013
22823013
22843013
(J)
dadddab
dadddab
bacccdc
bacccdc
aabbbcb
aabbbcb
badddcd
badddcd
daaddac
daaddac
aabbbcb
daaddac
aabbbcb
daaddac
badcddd
badcddd
caaccad
aabbbcb
aabbbcb
badddca
aaccbdd
abbddba
(L)
aabbbcb
aabbbcb
aabbbcb
aabbbcb
bacdadd
abcbddd
abbddba
aaccbdd
abdddcb
abccbdd
abdddbc
abdddcb
abbccdd
abbccdd
aadbdcb
aadbdcb
aadbdcb
aadbdcb
aadcdbc
aadbdcb
abcdbdd
abcbddd
abcdbdd
abcbddd
aadbdcd
badcddd
aabadcb
aabadcb
abcccdc
aabadcb
(M)
babbcdd
babbcdd
abccccc
abccccc
abccccc
abccccc
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
babbcbb
babbcbb
aacaaab
aacaaab
cabdddd
cabdddd
dadbcdd
aacbbba
aacbbba
aacbdba
aacbdba
cabdddd
cabdddd
dadbcdd
dbdacdd
aadaaab
aadaaab
aabcbba
aabcbba
abcbcda
aabcbba
abddddd
aaccdad
abddddd
abcbbbb
badddcd
badddcd
aadbdcd
badcddd
abddddd
abddddd
aaccdad
abddddd
alg.
21763013
21783013
21803013
21823013
21843013
21863013
21883013
21903013
21923013
21943013
21963013
21983013
22003013
22023013
22063013
22113013
22153013
22213013
22253013
22283013
22303013
22323013
22343013
22363013
22383013
22403013
22423013
22443013
22463013
22483013
22503013
22523013
22543013
22563013
22583013
22613013
22633013
22653013
22673013
22693013
22713013
22733013
22773013
22793013
22813013
22833013
22853013
155
(J)
(L)
bacccdc
bacccdc
badddcd
badcddd
badddcd
badcddd
caaccad
aabbbcb
caaccad
caaccad
aaccbdd
abbddba
abbcddd
daccadd
aabbbcb
bacdadd
abcbddd
aacaaab
aacaaab
cabdddd
dadbcdd
aacdbda
aacdbda
abcbbbb
abcbbbb
cabdddd
cabdddd
dadbcdd
aaccbdd
baccbdd
dbccbdd
dbccbdd
aadbdcb
aadbdcb
aadbdcb
aadbdcb
(M)
babbcdd
babbcdd
abccccc
abccccc
abccccc
abccccc
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
babbcbb
daaabac
aadbdcd
aadbdcd
aadbdcb
aaccdad
badddcd
badcddd
aadbdcd
badcddd
aadbdcb
aadbdcb
aadbdcd
badcddd
aaccdad
badddcd
aacccbc
aadbdcd
badcddd
aacbccc
aadaaab
aadaaab
badadcb
bacbdcc
baccccc
abddddd
bacbbbb
abddddd
abcadbb
badadcb
abddddd
abddddd
bacbbbb
abddddd
abcbbbb
156
alg.
22863013
22883013
22903013
22933013
22973013
22993013
23013013
23033013
23053013
23073013
23093013
23113013
23133013
23153013
23173013
23193013
23223013
23243013
23263013
23293013
23313013
23333013
23353013
23373013
23393013
23413013
23473013
23503013
23523013
23543013
23563013
23583013
23603013
23633013
23693013
23733013
23773013
23793013
23813013
23833013
23853013
23873013
23893013
23913013
23943013
23973013
23993013
ROGER D. MADDUX
(J)
bbcdcbc
(L)
cabbbdb
badddcd
baaddac
aacccbc
aacccbc
baaddac
daaddac
aadbdcb
aadbdcb
aadccbc
aadcdbc
aadccbc
aadcdbc
aadbdcb
aadccbc
aadbdcb
aadbdcd
aadbdcd
aacbccc
aacbccc
badcddd
aadbdcb
aadbdcb
aadcdbc
aadddbc
aadddbc
aadddbc
aadddbc
aadbdcb
abccbdd
aadddbc
aadddbc
bbcdcbc
aadcccd
aadcccd
abcccdc
abcccdc
aabadcb
abcccdc
aabadcb
abcccdc
aabcbba
abcbcda
bacbbbb
bacbbbb
abcadbb
abcadbb
dabddbb
cabbbdb
cabbbdb
aacccbc
aacccbc
abbccdd
bccddca
aacbccc
aacbccc
abbddbc
abbddbc
aaccdad
badddcd
abddddd
abddddd
abddddd
abddddd
aadbdca
aadccab
abcbbbb
abcbbbb
abcbbbb
abcbbbb
aabcbba
abcbcda
bacbdcc
baccccc
abcbddd
bbcdcbc
bccddca
dbdddac
abbddbc
(M)
abcbbbb
abcbbbb
abcbddc
abcbddc
abcbddd
aadbdcd
badcddd
abcbbbb
abcbbbb
abcbbbb
abcbbbb
aacddab
aacddab
aacddab
aacddab
cabdddd
cabdddd
cabdddd
dadbcdd
dadbcdd
dacdabb
abddddd
alg.
22873013
22893013
22913013
22943013
22983013
23003013
23023013
23043013
23063013
23083013
23103013
23123013
23143013
23163013
23183013
23213013
23233013
23253013
23273013
23303013
23323013
23343013
23363013
23383013
23403013
23453013
23493013
23513013
23533013
23553013
23573013
23593013
23613013
23653013
23713013
23753013
23783013
23803013
23823013
23843013
23863013
23883013
23903013
23923013
23953013
23983013
24003013
(J)
daaddac
aacccbc
aacccbc
badddcd
badddcd
aacbccc
aacbccc
aadbdcd
badcddd
badddcd
badcddd
aadbdcb
aadbdcb
acccdad
acccdad
bacbcad
bacbcad
aadbdcb
aadbdcb
aadcdbc
aadbdcb
aadccbc
aadbdcb
cbbccdd
aadddbc
aadddbc
(L)
aadcccd
aadcccd
cabbbdb
aabadcb
abcccdc
aabadcb
abcccdc
(M)
abcbbbb
abddddd
abddddd
abddddd
abddddd
aadbdca
aadccca
abcbbbb
abcbbbb
abcbbbb
abcbbbb
aabcbba
abcbcda
aabcbba
abcbcda
bacbdcc
baccccc
dabddbb
abcbbbb
abcbbbb
aadbdcb
aadddbc
aadddbc
aacccbc
aadddbc
aacccbc
aadddbc
aacccbc
abdddbc
aacccbc
abbccdd
bccddcb
bccddcb
dbdddac
bccddca
abbddbc
bccddca
dbdddba
aaccdad
daaddbc
aacbccc
aacbccc
bacbbbb
bacbbbb
abcbbbb
abcbbbb
abcbbbb
abcbbbb
aacbccc
abcbddd
aacbccc
abcbddd
aacddad
aacddad
aacddad
aacddad
cabdddd
cabdddd
cabdddd
dadbcdd
dadbcdd
abddddd
FINITE INTEGRAL RELATION ALGEBRAS
alg.
24013013
24033013
24073013
24093013
24113013
24133013
24153013
24173013
24193013
24213013
24233013
24273013
24313013
24333013
24353013
24373013
24393013
24413013
24433013
24453013
24473013
24493013
24513013
24533013
24553013
24583013
24603013
24633013
24693013
24743013
24763013
24783013
24803013
24833013
24873013
24913013
24973013
25013013
25123013
25163013
25263013
25283013
25323013
25363013
25543013
25583013
25613013
(J)
(L)
aadbbcb
aadbbcb
aadbdcd
badcddd
aaccdad
aaccdad
aadccbc
badddcd
aadccbc
daaddac
abddcbc
baaddac
abddcbc
daaddac
baaddac
daaddac
aadbbcb
aadbbcb
aadbbcb
aadbbcb
aadbbcb
aadbdcd
aadbdcd
badcddd
badcddd
aadbdcd
aadbdcd
abcbddc
badcddd
aabadcb
aadbbcb
aadbbcb
aadddbc
aadddbc
aadddbc
aadbbcb
aadccbc
aadddbc
aadccbc
aadddbc
aadddbc
aadddbc
accddcb
abbddbc
abbddbc
aacccbc
aacccbc
aacccbc
aaccdbd
aacccbc
aacddbd
aacdcac
aacddbd
aacddbd
(M)
abcadbb
badadcb
abddddd
abddddd
aadcdba
dacdabb
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
aadbbac
aadbdca
aadbbac
aadccab
abbadbc
cabddcc
dabddcc
dabddcc
dacbdcc
dabddbb
abcadbb
dabcdbb
dabddbb
dabcdbb
bbcddba
bbcddba
abcbddc
aacbccc
aacbccc
aacbccc
aadbdcd
aacbccc
aadbdcd
aacbcdc
aacbcdc
aadbdcd
alg.
24023013
24043013
24083013
24103013
24123013
24143013
24163013
24183013
24203013
24223013
24243013
24283013
24323013
24343013
24363013
24383013
24403013
24423013
24443013
24463013
24483013
24503013
24523013
24543013
24573013
24593013
24613013
24653013
24733013
24753013
24773013
24793013
24813013
24853013
24893013
24933013
24993013
25033013
25133013
25183013
25273013
25293013
25343013
25383013
25553013
25593013
25633013
157
(J)
(L)
badddcd
badddcd
aadbdcd
badcddd
aaccdad
aaccdad
aadccbc
daaddbc
bbcdcdd
badddcd
badddcd
badddcd
aadbdcd
aadbdcd
badcddd
badddcd
badcddd
aadbdcb
aadbdcb
aadbdcb
aadbdcb
aadbbcb
aadbbcb
acdddcb
aadbbcb
aadddbc
aadddbc
aadddbc
aadbbcb
aadccbc
aadddbc
aadccbc
aadddbc
aadccbc
aadccbc
abbddbc
abbddbc
accddcb
daaddac
bbcdcbc
aacccbc
bbccdbd
bbccdbd
aacccbc
aacddbd
aacdcac
baaccbc
aacddbd
bbcdcdd
aabadcb
aabadcb
(M)
abddddd
abddddd
abddddd
aadcdba
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
abddddd
aadbbac
aadbdca
aadbbac
cabddcc
abbadbc
dabddcc
abbadbc
bacddbb
bacddbb
abcadbb
abcbddd
bacddbb
bacddbb
bacddbb
bacddbb
bbcddba
bbcddba
abcbddc
abcbddd
aacbccc
aacbccc
aadbdcd
aacbcdc
aadbdcd
158
alg.
25653013
25733013
25753013
25823013
25863013
25923013
26053013
26113013
26133013
26153013
26193013
26213013
26233013
26253013
26283013
26313013
26353013
26393013
26413013
26433013
26453013
26473013
26493013
26523013
26543013
26563013
26603013
26623013
26643013
26663013
26683013
26703013
26723013
26743013
26773013
26793013
26823013
26843013
26863013
26923013
26943013
26963013
26983013
27033013
27083013
27113013
27153013
ROGER D. MADDUX
(J)
abbddbc
bbccdbd
bbccdbd
aacddbd
aacddbd
abbddbc
abbccbd
(L)
(M)
aadbdcd
aadbdcd
babbcbb
babbcbb
aabccca
aacaaab
abccccc
abccccc
accddca
accddca
caaddab
caaddab
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
bacccdc
bacccdc
bacccdc
bacccdc
abbbcbd
aacbbdb
abbbcbd
abbbcbd
acdaccb
babbcbb
acdaccb
babbcbb
abdaaaa
dbcdddd
babbccc
dbcdddd
babbccc
abccccc
abccccc
abccccc
abccccc
cddbdbc
babbcbb
dbcdddd
babbcbb
aacbcca
babbcbb
dbcdddd
dbcdddd
dbcdddd
dbcdddd
dbcdddd
dbcdddd
aabbbcb
aacbbdb
aabbbcb
abbbcbd
babbccc
babbccc
abccccc
alg.
25723013
25743013
25803013
25843013
25883013
26023013
26083013
26123013
26143013
26173013
26203013
26223013
26243013
26263013
26293013
26333013
26373013
26403013
26423013
26443013
26463013
26483013
26513013
26533013
26553013
26593013
26613013
26633013
26653013
26673013
26693013
26713013
26733013
26753013
26783013
26813013
26833013
26853013
26913013
26933013
26953013
26973013
26993013
27073013
27093013
27123013
27163013
(J)
aaccdbd
aaccdbd
aacddbd
aacddbd
abbddbc
abbccbd
abbccbd
(L)
aadbdcd
aadbdcd
aadbdcd
aadbdcd
(M)
babbcbb
babbcbb
aabccca
aacaaab
abccccc
abccccc
accddca
accddca
caaddac
caaddac
daaabac
daaabac
daaabac
daaabac
daacdab
daacdab
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aacbbdb
abbbcbd
aacbbdb
abbbcbd
aacbbdb
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
abbbcbd
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aabbbcb
daacdab
daacdab
aabbbcb
bacccdc
bacccdc
aadaaab
aadaaab
aadaaab
aadaaab
cabcccc
babbccc
dbcdddd
babbccc
abccccc
abccccc
abccccc
abccccc
aacbcca
aacbcca
dbcdddd
babbcbb
aacbcca
babbcbb
babbcbb
dbcdddd
dbcdddd
dbcdddd
dbcdddd
dbcdddd
dbcdddd
babbccc
babbccc
abccccc
FINITE INTEGRAL RELATION ALGEBRAS
alg.
27173013
27193013
27213013
27233013
27253013
27273013
27293013
27313013
27333013
27363013
27383013
27413013
27443013
27463013
27493013
27623013
27703013
27753013
27793013
27833013
27853013
27873013
27893013
27913013
27943013
27963013
27983013
28003013
28023013
28063013
28103013
28123013
28143013
28163013
28233013
28253013
28283013
28303013
28343013
28423013
28443013
28473013
28513013
28543013
28613013
28693013
28753013
(J)
abbbcbd
aacbbdb
abbbcbd
(L)
abbbcbd
abbbcbd
abbbcbd
bacccdc
bacccdc
bacccdc
bacccdc
abbbcbd
aacbbdb
abbbcbd
abbbcbd
abbbcbd
aacbbdb
abbbcbd
abbbcbd
(M)
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
aacbcca
babbcbb
aacbcca
babbcbb
aabbbcb
aabbbcb
bccddca
bccddca
aadbbcb
aadccbc
daaabac
aadbbcb
aadccbc
aadbbcb
aadbbcb
aadbbcb
aadbbcb
abddcbc
abddcbc
aadbbcb
aadccbc
aadbbcb
aadccbc
aadccbc
aadbbcb
accddcb
aadbbcb
aadbbcb
aadbbcb
aadbbcb
abbddbc
abbddbc
aabbbcb
aabbbcb
daaabac
daaabac
daaabac
aadaaab
aadaaab
aadaaab
aadaaab
aadaaab
abdabbc
dbcdddd
abdabbc
dbcdddd
abdabbc
abdabbc
dbcdddd
dbcdddd
dbcdddd
abcabbc
abcbcca
abdabbc
abdabbc
alg.
27183013
27203013
27223013
27243013
27263013
27283013
27303013
27323013
27343013
27373013
27403013
27423013
27453013
27483013
27583013
27663013
27743013
27783013
27823013
27843013
27863013
27883013
27903013
27933013
27953013
27973013
27993013
28013013
28033013
28073013
28113013
28133013
28153013
28223013
28243013
28263013
28293013
28313013
28383013
28433013
28463013
28503013
28523013
28553013
28653013
28713013
28773013
159
(J)
(L)
bacccdc
bacccdc
aabbbcb
aabbbcb
aabbbcb
aabbbcb
aacbbdb
abbbcbd
abbbcbd
aacbbdb
abbbcbd
abbbcbd
abbbcbd
aabbbcb
aabbbcb
abbddbc
abbddbc
aadbbcb
aadccbc
daaabac
aadbbcb
aadccbc
abbbcbd
aabbbcb
aabbbcb
abcbddc
abcbddc
babacad
babacad
babacad
aadbbcb
aadbbcb
(M)
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
abccccc
aacbcca
babbcbb
babbcbb
aacbcca
babbcbb
babbcbb
abcabbc
abcbcca
dbcdddd
abcabbc
abcbcca
aadaaab
dbcdddd
dbcdddd
dbcdddd
dbcdddd
aadbbcb
aadbbcb
aadbbcb
aadccbc
daaabac
aadbbcb
aadccbc
aadccbc
aadbbcb
aadbbcb
aadbbcb
accddcb
aadbbcb
aadbbcb
accddcb
accddcb
babacad
babacad
babacad
dbcdddd
dbcdddd
dbcdddd
abcabbc
abcbcca
abdabbc
abdabbc
160
ROGER D. MADDUX
alg.
28813013
28833013
28893013
28913013
28933013
28953013
29053013
29073013
29123013
29143013
29163013
29403013
29483013
29773013
(J)
caaddbd
caaddbd
cadddbd
cadddbd
(L)
aadbdcd
aadbdcd
cadbddd
cadbddd
caaddbd
caaddbd
cadddbd
aadbdcd
aadbdcd
cadbddd
baaccbc
baaccbc
aabccdc
aacbcdc
aacbcdc
aacbccc
(M)
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
alg.
28823013
28843013
28903013
28923013
28943013
28963013
29063013
29113013
29133013
29153013
29393013
29473013
29753013
29833013
(J)
caaddbd
caaddbd
cadddbd
cadddbd
(L)
aadbdcd
aadbdcd
cadbddd
cadbddd
caaddbd
cadddbd
cadddbd
aadbdcd
cadbddd
cadbddd
baaccbc
baaccbc
aabccdc
aabccdc
aacbcdc
aacbcdc
aacbccc
aacbccc
(M)
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
acddddd
19. 5-dimensional basis data for 11316 –13161316 and 13013 –30133013
alg.
11316
41316
71316
101316
131316
161316
191316
221316
251316
281316
311316
341316
371316
401316
431316
461316
491316
521316
551316
581316
611316
641316
671316
701316
731316
761316
791316
821316
851316
a
c
5
6
5 8
5 7
5 8
5 7
5 7
5 8
5 5
5 7
5 6
5 7
5 7
5 8
5 8
5 10
5 5
5 5
5 5
5 7
5 7
5 7
5 8
5 6
5 8
5 8
5 9
5 10
5 4
5 7
q
14
22
13
23
18
13
23
11
18
12
19
20
29
28
39
11
10
13
19
22
21
27
17
27
26
36
43
6
20
b
14
22
13
23
16
11
21
11
18
12
19
20
29
0
38
11
10
13
19
22
21
27
0
27
0
0
0
6
20
f
2
2
2
1
alg.
21316
51316
81316
111316
141316
171316
201316
231316
261316
291316
321316
351316
381316
411316
441316
471316
501316
531316
561316
591316
621316
651316
681316
711316
741316
771316
801316
831316
861316
a
c
5
7
5
6
5
8
5
8
5
8
5
8
5
9
5
6
5
5
5
7
5
7
5
8
5
8
5
9
5
4
5
6
5
5
5
6
5
5
5
5
5
6
5
6
5
7
5
7
5
9
5 10
5 11
5
5
5
7
q
18
9
17
23
24
19
29
14
8
15
20
24
26
35
8
14
10
16
12
11
17
16
24
23
33
45
52
10
19
b
18
9
17
23
24
19
29
14
8
15
20
24
0
34
8
14
10
16
10
9
15
16
24
0
32
0
0
10
19
f
1
2
2
2
1
alg.
31316
61316
91316
121316
151316
181316
211316
241316
271316
301316
331316
361316
391316
421316
451316
481316
511316
541316
571316
601316
631316
661316
691316
721316
751316
781316
811316
841316
871316
a
c
5
7
5
7
5
7
5
9
5
9
5
9
5 10
5
6
5
6
5
6
5
8
5
7
5
9
5
9
5
5
5
4
5
6
5
6
5
6
5
6
5
7
5
7
5
7
5
8
5
9
5 11
5 12
5
6
5
8
q
18
13
19
27
30
25
35
15
11
16
23
22
33
32
11
7
13
16
17
16
22
19
20
30
34
54
61
16
23
b
18
13
19
27
30
25
35
15
11
16
23
0
33
0
11
7
13
16
17
16
22
19
0
29
34
54
59
16
23
f
1
2
FINITE INTEGRAL RELATION ALGEBRAS
alg.
881316
911316
941316
971316
1001316
1031316
1061316
1091316
1121316
1151316
1181316
1211316
1241316
1271316
1301316
1331316
1361316
1391316
1421316
1451316
1481316
1511316
1541316
1571316
1601316
1631316
1661316
1691316
1721316
1751316
1781316
1811316
1841316
1871316
1901316
1931316
1961316
1991316
2021316
2051316
2081316
2111316
2141316
2171316
2201316
2231316
2261316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
b
8
29
0
10
41 41
7
23 23
8
29
0
7 26
0
9 37
0
9 38
0
9 35
35
9 42
41
9 36
36
9 49
49
11 63
63
5 13
13
7 19
19
8 32
32
6 18
0
6 20
0
8 27
0
7 23
0
8 35
35
7 26
26
8 41
41
7 21
0
9 34
34
9 45
45
11 65
0
11 65
0
13 86
84
7 26
26
9 34
34
10 52
52
9 38
38
10 51
0
11 62
62
7 27
27
9 37
32
11 67
66
9 47
0
11 65
0
11 65
0
11 71
0
11 73
0
13 94
0
12 74
0
13 101 101
13 82
0
14 118 118
f
1
2
5
1
alg.
891316
921316
951316
981316
1011316
1041316
1071316
1101316
1131316
1161316
1191316
1221316
1251316
1281316
1311316
1341316
1371316
1401316
1431316
1461316
1491316
1521316
1551316
1581316
1611316
1641316
1671316
1701316
1731316
1761316
1791316
1821316
1851316
1881316
1911316
1941316
1971316
2001316
2031316
2061316
2091316
2121316
2151316
2181316
2211316
2241316
2271316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
9
6
8
8
8
8
10
8
10
9
10
3
6
7
9
6
7
6
8
8
8
8
8
8
10
11
12
5
8
9
11
10
11
12
8
10
11
10
10
12
11
12
10
11
11
12
4
q
33
19
27
29
33
34
45
38
52
30
59
5
16
24
35
17
24
20
30
31
29
34
31
42
55
62
77
10
32
41
58
46
59
70
43
47
71
59
59
77
68
85
50
77
58
94
10
161
b
0
19
0
0
0
0
45
37
52
0
59
5
16
0
35
17
0
0
0
0
29
33
31
42
55
0
0
7
32
0
58
46
0
70
43
47
71
0
0
0
0
0
0
0
0
0
10
f
1
1
3
alg.
901316
931316
961316
991316
1021316
1051316
1081316
1111316
1141316
1171316
1201316
1231316
1261316
1291316
1321316
1351316
1381316
1411316
1441316
1471316
1501316
1531316
1561316
1591316
1621316
1651316
1681316
1711316
1741316
1771316
1801316
1831316
1861316
1891316
1921316
1951316
1981316
2011316
2041316
2071316
2101316
2131316
2161316
2191316
2221316
2251316
2281316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
9
37
7
23
7
25
9
33
8
30
9
41
8
31
9
48
8
26
10
40
10
53
4
8
6
16
8
27
5
14
7
21
7
23
7
27
7
28
9
38
7
31
9
44
8
24
9
52
10
53
12
74
12
74
6
16
8
28
10
47
8
30
9
43
10
54
6
17
9
53
10
57
12
81
10
53
11
71
10
59
12
80
12
82
11
62
12
89
12
70
13 106
8
33
b
37
0
0
0
0
41
31
48
0
40
53
8
16
0
14
0
0
0
0
38
30
44
0
52
0
72
0
16
28
0
0
0
0
0
53
0
81
0
0
0
0
0
0
0
0
0
33
f
1
2
162
alg.
2291316
2321316
2351316
2381316
2411316
2441316
2471316
2501316
2531316
2561316
2591316
2621316
2651316
2681316
2711316
2741316
2771316
2801316
2831316
2861316
2891316
2921316
2951316
2981316
3011316
3041316
3071316
3101316
3131316
3161316
3191316
3221316
3251316
3281316
3311316
3341316
3371316
3401316
3431316
3461316
3491316
3521316
3551316
3581316
3611316
3641316
3671316
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
9
8
10
10
10
11
11
12
10
12
12
11
11
13
12
13
8
10
10
10
10
12
10
11
10
12
12
10
10
12
11
12
9
11
11
11
12
11
11
13
11
12
11
13
13
11
11
q
35
27
47
53
49
64
69
86
53
73
80
61
68
91
81
104
41
54
56
63
62
81
61
81
69
92
90
61
64
81
77
90
52
68
73
77
90
81
85
105
77
97
86
112
113
83
86
b
0
27
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
90
0
0
0
0
0
86
112
113
0
0
f
alg.
2301316
2331316
2361316
2391316
2421316
2451316
2481316
2511316
2541316
2571316
2601316
2631316
2661316
2691316
2721316
2751316
2781316
2811316
2841316
2871316
2901316
2931316
2961316
2991316
3021316
3051316
3081316
3111316
3141316
3171316
3201316
3231316
3261316
3291316
3321316
3351316
3381316
3411316
3441316
3471316
3501316
3531316
3561316
3591316
3621316
3651316
3681316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
9
10
10
11
11
11
12
12
11
11
13
11
12
11
13
13
9
9
11
10
11
9
11
11
11
11
13
10
11
10
12
12
10
10
12
12
13
11
12
10
12
12
12
12
14
11
12
q
41
50
51
65
55
62
75
80
61
68
92
62
79
72
93
101
49
51
64
60
73
56
73
74
84
82
105
60
73
66
89
89
60
65
81
88
101
77
97
69
89
93
101
102
128
80
98
b
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
88
101
0
0
0
0
0
101
102
128
74
0
f
6
alg.
2311316
2341316
2371316
2401316
2431316
2461316
2491316
2521316
2551316
2581316
2611316
2641316
2671316
2701316
2731316
2761316
2791316
2821316
2851316
2881316
2911316
2941316
2971316
3001316
3031316
3061316
3091316
3121316
3151316
3181316
3211316
3241316
3271316
3301316
3331316
3361316
3391316
3421316
3451316
3481316
3511316
3541316
3571316
3601316
3631316
3661316
3691316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
10
9
11
12
10
12
11
13
11
12
10
12
12
12
12
14
9
10
9
11
11
10
10
12
11
12
9
11
11
11
11
13
10
11
10
11
10
12
12
11
11
13
12
13
10
12
12
q
50
38
63
77
53
73
71
95
65
80
53
70
80
84
89
116
46
59
52
71
70
68
69
86
77
97
52
69
72
78
78
101
60
73
66
79
69
89
93
81
85
105
97
117
71
92
95
b
50
0
63
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
79
0
0
0
0
0
0
97
117
0
92
95
f
FINITE INTEGRAL RELATION ALGEBRAS
alg.
3701316
3731316
3761316
3791316
3821316
3851316
3881316
3911316
3941316
3971316
4001316
4031316
4061316
4091316
4121316
4151316
4181316
4211316
4241316
4271316
4301316
4331316
4361316
4391316
4421316
4451316
4481316
4511316
4541316
4571316
4601316
4631316
4661316
4691316
4721316
4751316
4781316
4811316
4841316
4871316
4901316
4931316
4961316
4991316
5021316
5051316
5081316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
12
13
11
11
12
11
13
13
12
13
13
14
6
8
8
9
10
11
11
12
11
12
11
12
7
12
13
10
11
10
12
12
9
9
11
10
11
9
11
11
11
11
13
11
11
11
q
b
107 107
99
97
117
0
92
92
67
0
102 102
65
0
89
0
121 121
90
0
125 125
100
0
144 144
28
28
37
0
43
43
50
50
52
0
74
74
63
0
72
0
72
0
81
73
80
80
89
0
26
26
65
0
80
0
69
69
63
63
61
61
90
90
94
94
39
0
41
0
54
0
56
0
66
0
44
0
61
0
61
0
75
0
71
0
96
0
68
0
59
0
76
0
f
2
8
alg.
3711316
3741316
3771316
3801316
3831316
3861316
3891316
3921316
3951316
3981316
4011316
4041316
4071316
4101316
4131316
4161316
4191316
4221316
4251316
4281316
4311316
4341316
4371316
4401316
4431316
4461316
4491316
4521316
4551316
4581316
4611316
4641316
4671316
4701316
4731316
4761316
4791316
4821316
4851316
4881316
4911316
4941316
4971316
5001316
5031316
5061316
5091316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
13
13
12
12
12
12
12
14
13
14
14
15
7
9
9
10
9
9
10
10
12
12
12
13
11
12
9
11
11
11
11
13
9
10
9
11
11
10
10
12
11
12
10
12
11
12
q
87
114
114
102
79
102
77
109
133
105
140
115
159
30
42
52
59
50
47
56
61
83
81
95
104
55
70
52
75
80
69
67
102
38
48
46
67
65
55
55
72
70
86
62
83
50
91
b
0
112
112
102
0
102
0
109
133
0
140
0
159
0
0
52
59
0
0
0
0
83
0
95
96
0
0
52
75
80
69
67
102
0
0
0
0
0
0
0
0
0
0
0
0
0
0
163
f
2
2
8
alg.
3721316
3751316
3781316
3811316
3841316
3871316
3901316
3931316
3961316
3991316
4021316
4051316
4081316
4111316
4141316
4171316
4201316
4231316
4261316
4291316
4321316
4351316
4381316
4411316
4441316
4471316
4501316
4531316
4561316
4591316
4621316
4651316
4681316
4711316
4741316
4771316
4801316
4831316
4861316
4891316
4921316
4951316
4981316
5011316
5041316
5071316
5101316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
12
14
13
11
13
12
13
11
12
12
13
5
8
7
8
9
10
10
11
11
11
13
13
14
11
12
10
10
12
11
12
8
10
10
10
10
12
10
11
10
12
12
11
10
12
12
q
102
102
129
112
90
114
77
121
75
110
85
129
21
35
34
41
44
62
55
64
72
70
92
110
119
43
58
58
57
86
82
75
32
45
47
57
55
76
50
66
60
85
81
77
44
65
82
b
0
0
127
112
90
114
0
121
0
110
0
129
21
0
29
36
0
62
0
0
72
0
84
110
111
0
0
58
57
86
82
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
2
5
5
8
8
164
alg.
5111316
5141316
5171316
5201316
5231316
5261316
5291316
5321316
5351316
5381316
5411316
5441316
5471316
5501316
5531316
5561316
5591316
5621316
5651316
5681316
5711316
5741316
5771316
5801316
5831316
5861316
5891316
5921316
5951316
5981316
6011316
6041316
6071316
6101316
6131316
6161316
6191316
6221316
6251316
6281316
6311316
6341316
6371316
6401316
6431316
6461316
6491316
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
11
13
12
13
9
11
10
10
11
11
12
11
12
12
10
10
11
11
11
11
13
11
12
12
12
12
13
13
11
9
11
10
11
10
11
10
12
12
11
10
12
11
12
11
13
11
q
97
80
109
72
113
45
59
49
54
65
55
71
65
69
79
46
48
58
61
57
60
92
66
81
82
78
79
102
99
75
57
77
48
85
70
91
58
86
94
70
62
84
81
95
83
105
61
b
0
0
109
0
113
0
0
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
82
0
0
0
94
0
0
0
0
85
70
91
0
86
85
0
0
0
0
0
0
0
0
f
5
9
alg.
5121316
5151316
5181316
5211316
5241316
5271316
5301316
5331316
5361316
5391316
5421316
5451316
5481316
5511316
5541316
5571316
5601316
5631316
5661316
5691316
5721316
5751316
5781316
5811316
5841316
5871316
5901316
5931316
5961316
5991316
6021316
6051316
6081316
6111316
6141316
6171316
6201316
6231316
6261316
6291316
6321316
6351316
6381316
6411316
6441316
6471316
6501316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
11
73
12
99
11
62
13
91
13 104
10
50
9
40
11
54
10
56
12
74
11
52
10
55
12
73
11
69
13
91
9
31
11
59
10
44
12
76
11
62
12
71
10
54
12
74
11
54
13
93
11
51
13
90
12
71
14 114
11
83
10
72
9
43
11
63
11
75
11
79
11
81
11
77
11
85
13 113
11
73
11
73
10
69
12
96
12
92
12
91
11
79
12
76
b
73
99
0
91
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
93
0
0
0
114
0
72
0
0
0
79
0
77
75
113
0
0
0
0
89
0
0
0
f
10
3
alg.
5131316
5161316
5191316
5221316
5251316
5281316
5311316
5341316
5371316
5401316
5431316
5461316
5491316
5521316
5551316
5581316
5611316
5641316
5671316
5701316
5731316
5761316
5791316
5821316
5851316
5881316
5911316
5941316
5971316
6001316
6031316
6061316
6091316
6121316
6151316
6181316
6211316
6241316
6271316
6301316
6331316
6361316
6391316
6421316
6451316
6481316
6511316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
12
12
12
14
10
10
9
11
10
11
11
11
12
9
10
10
11
10
12
12
11
11
12
11
12
12
13
10
12
10
10
10
12
10
12
11
12
10
12
11
11
11
13
12
12
12
q
83
90
81
94
123
54
45
45
65
47
59
63
59
81
38
42
47
59
49
73
77
62
70
65
67
62
87
86
70
88
62
58
70
90
72
100
67
104
62
81
73
84
80
107
97
94
93
b
83
0
81
0
123
0
0
0
0
0
0
0
0
0
0
30
0
59
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
0
104
0
0
0
0
0
107
0
0
0
f
12
FINITE INTEGRAL RELATION ALGEBRAS
alg.
6521316
6551316
6581316
6611316
6641316
6671316
6701316
6731316
6761316
6791316
6821316
6851316
6881316
6911316
6941316
6971316
7001316
7031316
7061316
7091316
7121316
7151316
7181316
7211316
7241316
7271316
7301316
7331316
7361316
7391316
7421316
7451316
7481316
7511316
7541316
7571316
7601316
7631316
7661316
7691316
7721316
7751316
7781316
7811316
7841316
7871316
7901316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
11
13
12
13
8
10
10
10
9
11
11
10
10
12
10
12
11
12
9
11
11
11
11
13
11
12
11
13
13
11
11
13
12
12
12
14
12
12
12
14
12
14
13
14
9
11
q
108
89
120
83
122
42
54
61
59
40
58
74
63
67
85
71
97
74
93
53
69
74
77
79
101
81
94
88
118
116
82
86
106
97
79
102
128
101
83
106
132
111
145
104
146
38
59
b
0
0
120
0
122
0
0
0
0
0
0
0
0
0
85
0
97
0
93
0
0
0
0
0
101
0
0
0
117
116
0
0
0
0
0
102
128
97
0
0
132
105
145
0
146
25
0
f
1
4
6
13
alg.
6531316
6561316
6591316
6621316
6651316
6681316
6711316
6741316
6771316
6801316
6831316
6861316
6891316
6921316
6951316
6981316
7011316
7041316
7071316
7101316
7131316
7161316
7191316
7221316
7251316
7281316
7311316
7341316
7371316
7401316
7431316
7461316
7491316
7521316
7551316
7581316
7611316
7641316
7671316
7701316
7731316
7761316
7791316
7821316
7851316
7881316
7911316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
12
11
13
13
9
9
11
10
10
10
12
10
11
10
11
10
12
12
10
10
12
11
12
10
12
12
12
12
14
11
12
11
13
12
13
11
13
12
13
12
13
12
14
14
10
10
q
82
108
71
102
115
46
53
65
63
47
63
81
67
74
63
82
59
85
97
61
66
82
77
90
70
92
94
103
101
131
78
98
86
112
75
117
90
116
79
121
98
130
89
123
142
48
47
b
82
108
0
102
106
0
0
0
0
0
0
81
0
0
0
82
0
85
97
0
0
0
0
90
0
0
94
102
101
131
0
0
0
0
0
117
0
116
0
0
98
130
0
123
142
39
0
165
f
9
1
9
alg.
6541316
6571316
6601316
6631316
6661316
6691316
6721316
6751316
6781316
6811316
6841316
6871316
6901316
6931316
6961316
6991316
7021316
7051316
7081316
7111316
7141316
7171316
7201316
7231316
7261316
7291316
7321316
7351316
7381316
7411316
7441316
7471316
7501316
7531316
7561316
7591316
7621316
7651316
7681316
7711316
7741316
7771316
7801316
7831316
7861316
7891316
7921316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
12
12
12
14
9
10
9
11
10
11
9
11
11
11
11
11
11
13
10
11
10
12
12
11
11
13
12
13
10
12
12
12
11
13
13
12
11
13
13
13
13
13
13
15
10
11
q
94
101
90
103
134
50
57
52
70
51
70
56
74
78
78
86
70
82
108
61
74
66
88
90
81
83
105
103
116
70
90
94
101
64
90
113
105
68
94
117
113
126
108
127
161
49
57
b
94
0
90
0
134
0
0
0
0
0
70
0
0
78
78
0
0
82
108
0
0
0
0
0
0
0
105
0
116
0
0
0
0
0
0
113
0
0
94
117
113
120
108
127
161
0
0
f
6
166
alg.
7931316
7961316
7991316
8021316
8051316
8081316
8111316
8141316
8171316
8201316
8231316
8261316
8291316
8321316
8351316
8381316
8411316
8441316
8471316
8501316
8531316
8561316
8591316
8621316
8651316
8681316
8711316
8741316
8771316
8801316
8831316
8861316
8891316
8921316
8951316
8981316
9011316
9041316
9071316
9101316
9131316
9161316
9191316
9221316
9251316
9281316
9311316
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
11
11
13
11
13
13
8
7
9
9
9
8
10
10
9
8
10
10
10
9
11
11
10
9
11
11
10
10
12
10
11
10
12
12
9
8
10
10
10
9
11
11
10
9
11
11
q
61
61
61
89
56
96
80
33
32
42
42
46
42
60
56
45
42
56
55
60
54
76
71
64
59
77
76
57
49
95
56
92
56
82
94
41
39
52
54
57
52
73
71
55
52
69
70
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
57
0
95
0
92
0
82
0
0
0
0
0
0
0
0
0
0
0
0
0
f
alg.
7941316
7971316
8001316
8031316
8061316
8091316
8121316
8151316
8181316
8211316
8241316
8271316
8301316
8331316
8361316
8391316
8421316
8451316
8481316
8511316
8541316
8571316
8601316
8631316
8661316
8691316
8721316
8751316
8781316
8811316
8841316
8871316
8901316
8931316
8961316
8991316
9021316
9051316
9081316
9111316
9141316
9171316
9201316
9231316
9261316
9291316
9321316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
12
71
11
62
12
73
11
66
12
81
12
74
14 114
8
36
8
39
8
39
10
49
9
46
9
53
9
49
11
67
9
47
9
53
9
52
11
66
10
59
10
69
10
64
12
86
10
66
10
74
10
73
12
91
10
66
11
64
9
49
11
75
11
80
11
75
11
87
13 113
9
46
9
46
9
48
11
61
10
59
10
63
10
61
12
82
10
59
10
63
10
64
12
81
b
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
61
0
0
0
0
64
0
75
0
75
0
113
0
0
0
0
0
0
0
0
0
0
0
0
f
5
alg.
7951316
7981316
8011316
8041316
8071316
8101316
8131316
8161316
8191316
8221316
8251316
8281316
8311316
8341316
8371316
8401316
8431316
8461316
8491316
8521316
8551316
8581316
8611316
8641316
8671316
8701316
8731316
8761316
8791316
8821316
8851316
8881316
8911316
8941316
8971316
9001316
9031316
9061316
9091316
9121316
9151316
9181316
9211316
9241316
9271316
9301316
9331316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
10
49
12
74
12
77
12
81
12
62
13
99
7
29
9
40
8
35
9
46
8
39
10
53
9
49
10
60
8
37
10
55
9
45
10
63
9
49
11
70
10
61
11
79
9
52
11
78
10
62
11
88
9
42
11
81
11
80
10
68
10
73
12
99
11
63
12 106
8
37
10
50
9
45
10
55
9
50
11
66
10
62
11
72
9
47
11
67
10
58
11
75
10
63
b
0
0
0
81
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
71
0
81
0
68
0
99
0
106
0
0
0
0
0
0
0
0
0
0
0
0
0
f
3
17
FINITE INTEGRAL RELATION ALGEBRAS
alg.
9341316
9371316
9401316
9431316
9461316
9491316
9521316
9551316
9581316
9611316
9641316
9671316
9701316
9731316
9761316
9791316
9821316
9851316
9881316
9911316
9941316
9971316
10001316
10031316
10061316
10091316
10121316
10151316
10181316
10211316
10241316
10271316
10301316
10331316
10361316
10391316
10421316
10451316
10481316
10511316
10541316
10571316
10601316
10631316
10661316
10691316
10721316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
10
12
12
10
9
11
11
11
10
12
12
11
10
12
12
11
11
13
11
12
11
13
13
10
9
11
11
11
10
12
12
11
10
12
12
12
11
13
13
12
11
12
11
13
13
12
q
74
68
93
90
56
52
69
70
74
67
92
89
77
72
93
94
69
62
114
71
109
69
98
116
55
52
68
73
74
68
92
93
72
68
88
92
94
87
115
115
96
71
106
66
90
119
86
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
114
0
109
0
98
0
0
0
0
0
74
0
92
89
0
0
0
0
94
0
115
110
96
0
106
0
0
0
86
f
alg.
9351316
9381316
9411316
9441316
9471316
9501316
9531316
9561316
9591316
9621316
9651316
9681316
9711316
9741316
9771316
9801316
9831316
9861316
9891316
9921316
9951316
9981316
10011316
10041316
10071316
10101316
10131316
10161316
10191316
10221316
10251316
4 10281316
10311316
10341316
10371316
10401316
10431316
10461316
10491316
5 10521316
10551316
10581316
10611316
10641316
10671316
10701316
10731316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
11
11
13
10
10
10
12
11
11
11
13
11
11
11
13
11
12
10
12
12
12
12
14
10
10
10
12
11
11
11
13
11
11
11
13
12
12
12
14
12
12
12
12
12
14
12
q
75
83
80
105
60
63
64
81
75
82
79
104
81
87
88
109
83
77
61
90
100
88
106
135
63
59
64
80
79
79
80
104
79
79
83
103
98
102
102
130
103
80
100
81
110
134
106
b
0
0
0
105
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
90
0
88
0
135
0
59
0
0
79
79
0
104
0
79
0
0
98
102
0
130
103
0
0
0
0
0
106
167
f
alg.
9361316
9391316
9421316
9451316
9481316
9511316
9541316
9571316
9601316
9631316
9661316
9691316
9721316
9751316
9781316
9811316
9841316
9871316
9901316
9931316
9961316
9991316
10021316
10051316
10081316
10111316
10141316
10171316
10201316
10231316
10261316
10291316
10321316
10351316
10381316
10411316
10441316
10471316
10501316
10531316
10561316
10591316
10621316
10651316
10681316
10711316
10741316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
11
12
9
11
10
11
10
12
11
12
10
12
11
12
10
12
12
11
11
13
12
13
9
11
10
11
10
12
11
12
10
12
11
12
11
13
12
13
11
13
11
13
12
13
11
13
q
86
78
95
48
68
58
75
63
86
77
94
65
93
78
103
54
98
99
80
90
119
79
125
51
67
61
71
67
86
81
91
64
87
77
94
83
109
100
117
84
115
91
115
75
125
71
121
b f
86
0
95
0
0
0
0
0
0
0
0
0
0
0
0
0
98
0
80
0
119
0
125
0
0
0
71
67
86
77 4
91
0
0
0
94
83
109
95
5
117
82
2
115
0
0
0
125
60 11
121
168
alg.
10751316
10781316
10811316
10841316
10871316
10901316
10931316
10961316
10991316
11021316
11051316
11081316
11111316
11141316
11171316
11201316
11231316
11261316
11291316
11321316
11351316
11381316
11411316
11441316
11471316
11501316
11531316
11561316
11591316
11621316
11651316
11681316
11711316
11741316
11771316
11801316
11831316
11861316
11891316
11921316
11951316
11981316
12011316
12041316
12071316
12101316
12131316
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
12
13
12
14
14
8
9
9
9
11
11
12
9
10
9
11
11
10
10
12
11
12
9
11
11
11
11
13
10
12
11
12
10
12
12
12
12
14
11
12
11
12
11
12
9
q
81
140
91
132
88
120
145
46
55
59
61
75
89
98
55
71
64
82
83
75
76
94
93
109
67
83
87
98
99
121
83
105
69
114
74
104
115
102
120
150
78
93
90
105
101
116
64
b
0
140
81
132
0
120
139
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
98
99
121
83
105
0
114
0
104
115
102
120
150
0
0
0
105
0
116
0
f
alg.
10761316
10791316
10 10821316
10851316
10881316
10911316
6 10941316
10971316
11001316
11031316
11061316
11091316
11121316
11151316
11181316
11211316
11241316
11271316
11301316
11331316
11361316
11391316
11421316
11451316
11481316
11511316
11541316
11571316
11601316
11631316
11661316
11691316
11721316
11751316
11781316
11811316
11841316
11871316
11901316
11931316
11961316
11991316
12021316
12051316
12081316
12111316
12141316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
11
13
13
13
13
15
9
10
9
10
9
10
8
10
10
10
10
12
10
11
10
12
12
10
10
12
11
12
10
11
10
12
12
11
11
13
12
13
9
10
10
12
12
12
13
10
q
96
78
110
126
107
132
164
50
59
59
68
67
76
51
63
67
75
76
94
71
87
82
108
105
79
83
99
90
114
60
98
62
84
106
93
104
134
94
139
62
77
79
101
105
116
131
72
b
96
0
110
120
107
0
164
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
114
0
98
0
84
106
93
104
134
0
139
0
0
0
0
0
0
131
0
f
alg.
10771316
10801316
10831316
6 10861316
10891316
10921316
10951316
10981316
11011316
11041316
11071316
11101316
11131316
11161316
11191316
11221316
11251316
11281316
11311316
11341316
11371316
11401316
11431316
11461316
11491316
11521316
11551316
11581316
11611316
11641316
11671316
11701316
11731316
11761316
11791316
11821316
11851316
11881316
11911316
11941316
11971316
12001316
12031316
12061316
12091316
12121316
12151316
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
12
12
14
13
14
7
8
8
10
10
10
11
9
9
11
10
11
9
11
11
11
11
13
10
11
10
12
12
11
11
11
11
13
11
12
11
13
13
10
11
11
11
13
13
14
11
q
125
97
113
145
101
151
42
51
52
66
68
78
87
59
63
75
71
87
64
82
83
97
94
120
71
95
83
105
106
75
90
77
99
121
85
123
83
113
131
70
85
90
94
116
131
146
80
b
125
97
0
145
0
151
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
105
106
0
90
0
99
121
0
123
0
113
131
0
0
0
0
116
0
146
0
f
FINITE INTEGRAL RELATION ALGEBRAS
alg.
12161316
12191316
12221316
12251316
12281316
12311316
12341316
12371316
12401316
12431316
12461316
12491316
12521316
12551316
12581316
12611316
12641316
12671316
12701316
12731316
12761316
12791316
12821316
12851316
12881316
12911316
12941316
12971316
13001316
13031316
13061316
13091316
13121316
13151316
23013
53013
83013
113013
143013
173013
203013
233013
263013
293013
323013
353013
383013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
10
10
12
12
11
12
12
13
11
11
13
12
13
11
12
11
13
13
12
12
14
13
14
11
12
12
13
12
14
14
13
14
14
15
7
7
9
8
9
7
8
8
9
7
9
8
10
q
79
80
102
106
87
116
95
131
94
101
121
113
136
76
117
76
102
132
109
127
161
116
165
104
127
98
143
97
127
166
131
176
145
199
18
18
26
22
26
18
22
22
26
19
29
23
33
b
0
0
102
0
0
116
0
131
0
0
0
0
136
0
0
0
102
132
109
127
161
0
165
100
127
92
143
0
127
166
131
176
145
199
18
18
26
22
26
16
20
20
24
17
29
21
33
f
4
6
2
2
2
2
2
2
alg.
12171316
12201316
12231316
12261316
12291316
12321316
12351316
12381316
12411316
12441316
12471316
12501316
12531316
12561316
12591316
12621316
12651316
12681316
12711316
12741316
12771316
12801316
12831316
12861316
12891316
12921316
12951316
12981316
13011316
13041316
13071316
13101316
13131316
13161316
33013
63013
93013
123013
153013
183013
213013
243013
273013
303013
333013
363013
393013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
11
11
13
12
13
13
14
11
12
11
13
13
12
12
12
12
14
12
13
12
14
14
12
13
13
13
13
13
15
14
15
15
16
7
8
7
9
9
8
9
9
10
8
9
9
10
q
87
91
95
117
102
131
110
146
90
113
102
128
132
91
113
91
121
147
105
146
101
135
161
116
139
113
143
112
151
181
150
195
164
218
18
22
18
26
26
24
28
28
32
25
31
29
35
b
0
91
0
117
102
131
110
146
0
0
0
128
132
0
113
0
0
147
0
146
0
135
161
114
139
108
143
112
151
181
150
195
164
218
18
22
18
26
26
24
28
28
32
25
31
29
35
169
f
alg.
12181316
12211316
12241316
12271316
12301316
12331316
12361316
12391316
12421316
12451316
12481316
12511316
12541316
12571316
12601316
12631316
12661316
12691316
12721316
12751316
12781316
12811316
12841316
2 12871316
12901316
5 12931316
12961316
12991316
13021316
13051316
13081316
13111316
13141316
13013
43013
73013
103013
133013
163013
193013
223013
253013
283013
313013
343013
373013
403013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
11
12
10
11
11
12
10
12
12
12
12
14
11
13
12
13
11
13
13
13
13
15
13
14
12
14
13
14
12
13
13
14
6
8
8
8
8
10
9
10
10
11
8
10
9
11
q
95
91
106
72
101
80
116
82
102
109
117
121
147
102
128
87
136
90
124
142
120
146
180
128
151
128
158
112
166
112
157
126
180
14
22
22
22
22
30
30
34
34
38
23
35
27
39
b
0
0
106
0
101
0
116
0
0
0
117
121
147
0
128
0
0
0
124
142
120
146
180
128
151
128
158
0
166
0
157
126
180
14
22
22
22
22
30
30
34
34
38
21
35
25
39
f
2
2
170
alg.
413013
443013
473013
503013
533013
563013
593013
623013
653013
683013
713013
743013
773013
803013
833013
863013
893013
923013
953013
983013
1013013
1043013
1073013
1103013
1133013
1163013
1193013
1223013
1253013
1283013
1313013
1343013
1373013
1403013
1433013
1463013
1493013
1523013
1553013
1583013
1613013
1643013
1673013
1703013
1733013
1763013
1793013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
7
9
9
10
9
12
12
9
10
11
10
11
13
14
4
7
7
10
10
10
11
10
10
12
9
9
8
10
10
10
10
12
11
12
10
11
10
12
12
11
11
14
6
9
9
10
9
q
20
30
28
36
30
54
50
30
36
42
41
45
61
74
8
19
21
32
36
43
47
36
42
51
28
27
26
42
39
38
35
51
50
54
44
55
40
59
56
60
53
86
15
32
29
40
40
b
18
30
26
36
0
54
0
28
34
42
0
0
61
0
8
19
21
32
36
43
47
0
0
0
0
0
0
42
0
0
0
0
50
54
40
55
0
59
53
60
53
86
15
32
29
40
40
f
2
2
2
2
4
3
alg.
423013
453013
483013
513013
543013
573013
603013
633013
663013
693013
723013
753013
783013
813013
843013
873013
903013
933013
963013
993013
1023013
1053013
1083013
1113013
1143013
1173013
1203013
1233013
1263013
1293013
1323013
1353013
1383013
1413013
1443013
1473013
1503013
1533013
1563013
1593013
1623013
1653013
1683013
1713013
1743013
1773013
1803013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
8
8
10
10
10
10
13
9
11
12
11
12
12
15
5
8
8
9
11
11
12
10
11
7
10
10
9
9
11
10
11
9
10
9
11
11
11
11
13
12
12
4
7
7
10
10
10
q
26
24
34
36
38
34
58
30
42
48
49
53
54
84
12
27
25
32
42
49
53
35
47
18
33
32
34
31
47
38
43
34
38
36
55
52
51
48
67
71
64
7
19
22
33
38
46
b
26
22
34
36
0
0
58
28
42
48
0
0
0
0
12
27
25
32
42
49
53
0
0
14
0
0
0
0
0
0
0
30
34
0
55
49
51
0
67
71
64
7
19
22
33
38
46
f
2
2
4
4
4
3
alg.
433013
463013
493013
523013
553013
583013
613013
643013
673013
703013
733013
763013
793013
823013
853013
883013
913013
943013
973013
1003013
1033013
1063013
1093013
1123013
1153013
1183013
1213013
1243013
1273013
1303013
1333013
1363013
1393013
1423013
1453013
1483013
1513013
1543013
1573013
1603013
1633013
1663013
1693013
1723013
1753013
1783013
1813013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
8
9
9
11
11
11
8
10
10
9
10
12
13
16
6
9
9
10
9
10
9
11
11
8
8
11
9
10
9
11
11
10
11
10
10
12
11
12
10
13
13
5
8
8
9
11
11
q
24
30
32
40
46
42
24
36
36
33
37
57
64
94
15
31
28
38
37
41
31
40
46
23
22
37
34
39
30
46
43
42
46
47
44
63
48
59
49
82
75
11
28
26
34
44
52
b
22
30
32
40
0
0
20
36
34
0
0
57
0
94
15
31
28
38
37
41
0
0
0
0
18
0
0
0
0
46
0
42
46
47
0
63
44
59
49
82
75
11
28
26
34
44
52
f
2
4
2
4
4
FINITE INTEGRAL RELATION ALGEBRAS
alg.
1823013
1853013
1883013
1913013
1943013
1973013
2003013
2033013
2063013
2093013
2123013
2153013
2183013
2213013
2243013
2273013
2303013
2333013
2363013
2393013
2423013
2453013
2483013
2513013
2543013
2573013
2603013
2633013
2663013
2693013
2723013
2753013
2783013
2813013
2843013
2873013
2903013
2933013
2963013
2993013
3023013
3053013
3083013
3113013
3143013
3173013
3203013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
10
44
9 33
11 42
11 49
8 25
8 24
11 39
9 37
10 42
9 33
11 49
11 46
10 45
11 49
10 51
10 48
12 67
11 52
12 63
10 54
13 87
13 80
14 89
14 86
17 125
7 22
10 47
10 39
11 55
8 32
11 51
10 51
11 57
7 24
10 53
9 35
13 74
13 84
11 57
13 78
13 88
14 99
8 32
10 41
12 55
11 57
12 63
b
44
0
0
0
0
20
0
0
0
0
49
0
45
49
51
0
67
48
63
54
87
80
0
0
122
0
47
0
55
32
0
45
51
0
53
0
74
84
57
76
88
99
32
0
0
57
0
f
4
4
3
6
6
2
alg.
1833013
1863013
1893013
1923013
1953013
1983013
2013013
2043013
2073013
2103013
2133013
2163013
2193013
2223013
2253013
2283013
2313013
2343013
2373013
2403013
2433013
2463013
2493013
2523013
2553013
2583013
2613013
2643013
2673013
2703013
2733013
2763013
2793013
2823013
2853013
2883013
2913013
2943013
2973013
3003013
3033013
3063013
3093013
3123013
3153013
3183013
3213013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
11
50
10
38
10
45
12
54
9
30
9
29
8
29
10
45
10
42
10
41
10
38
12
54
11
53
12
57
10
48
11
59
10
44
12
63
12
60
11
65
11
58
14
91
15 102
15
99
5
12
8
28
7
22
11
45
11
53
9
38
11
51
11
61
12
67
8
35
11
69
10
46
12
73
14
95
12
67
14
87
14 101
15 112
8
30
11
49
10
49
12
65
12
63
b
50
0
0
0
0
0
0
45
0
0
0
0
53
57
44
59
0
63
57
65
58
91
0
0
8
0
0
0
53
38
0
61
67
35
69
46
73
95
0
86
101
112
0
0
0
65
63
171
f
4
3
4
1
alg.
1843013
1873013
1903013
1933013
1963013
1993013
2023013
2053013
2083013
2113013
2143013
2173013
2203013
2233013
2263013
2293013
2323013
2353013
2383013
2413013
2443013
2473013
2503013
2533013
2563013
2593013
2623013
2653013
2683013
2713013
2743013
2773013
2803013
2833013
2863013
2893013
2923013
2953013
2983013
3013013
3043013
3073013
3103013
3133013
3163013
3193013
3223013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
12
56
10
37
11
50
7
20
10
35
10
34
9
37
9
34
11
50
10
41
11
46
9
37
10
41
9
40
11
59
11
56
11
55
11
52
13
71
12
76
12
69
13
76
16 115
16 112
6
18
9
41
8
28
10
47
12
61
10
45
12
57
12
71
13
77
9
42
12
80
12
63
13
84
10
46
13
76
12
75
13
86
7
24
9
38
11
47
11
57
11
55
13
71
b
56
0
0
16
0
0
0
0
0
0
0
33
37
0
59
53
55
0
71
76
69
0
0
0
18
41
28
47
61
0
0
71
77
38
80
0
84
37
0
71
82
0
38
0
0
0
71
f
4
4
4
3
4
9
4
4
172
alg.
3233013
3263013
3293013
3323013
3353013
3383013
3413013
3443013
3473013
3503013
3533013
3563013
3593013
3623013
3653013
3683013
3713013
3743013
3773013
3803013
3833013
3863013
3893013
3923013
3953013
3983013
4013013
4043013
4073013
4103013
4133013
4163013
4193013
4223013
4253013
4283013
4313013
4343013
4373013
4403013
4433013
4463013
4493013
4523013
4553013
4583013
4613013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
15
12
14
14
13
13
15
14
15
13
15
15
14
14
16
15
16
8
10
12
10
11
12
12
13
14
13
15
15
16
14
15
16
7
12
12
12
14
14
15
13
15
12
13
q
56
76
80
108
60
82
83
78
79
100
85
101
78
103
101
101
98
127
108
124
34
47
61
53
61
69
66
79
92
83
107
108
121
105
118
131
32
77
84
82
98
112
118
96
114
79
86
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
120
0
0
0
0
55
63
0
0
0
0
0
0
121
0
0
131
32
77
84
82
98
112
118
96
114
0
0
f
4
6
6
alg.
3243013
3273013
3303013
3333013
3363013
3393013
3423013
3453013
3483013
3513013
3543013
3573013
3603013
3633013
3663013
3693013
3723013
3753013
3783013
3813013
3843013
3873013
3903013
3933013
3963013
3993013
4023013
4053013
4083013
4113013
4143013
4173013
4203013
4233013
4263013
4293013
4323013
4353013
4383013
4413013
4443013
4473013
4503013
4533013
4563013
4593013
4623013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
15
13
13
15
13
14
13
15
15
14
14
16
14
15
14
16
16
9
11
12
11
12
13
13
14
15
14
14
16
16
15
16
17
10
13
12
13
12
13
12
14
11
13
13
q
69
73
93
102
69
70
92
75
91
76
97
98
90
88
113
98
114
95
124
121
42
53
63
63
71
79
75
88
101
95
96
120
121
121
134
147
65
83
84
90
90
96
88
106
71
89
84
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
109
0
0
0
0
0
42
0
0
0
71
79
0
0
0
0
0
0
0
0
0
147
65
83
84
90
90
96
88
106
0
89
0
f
4
alg.
3253013
3283013
3313013
3343013
3373013
3403013
3433013
3463013
3493013
3523013
3553013
3583013
3613013
3643013
3673013
3703013
3733013
3763013
3793013
3823013
3853013
3883013
3913013
3943013
3973013
4003013
4033013
4063013
4093013
4123013
4153013
4183013
4213013
4243013
4273013
4303013
4333013
4363013
4393013
4423013
4453013
4483013
4513013
4543013
4573013
4603013
4633013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
14
16
13
14
12
14
14
14
14
16
14
15
13
15
15
15
15
17
10
11
13
12
13
14
14
15
16
14
15
15
17
16
17
18
11
11
13
13
13
14
13
14
12
12
14
q
63
86
95
115
73
79
66
87
88
88
89
110
91
100
85
114
111
111
108
137
50
55
69
73
81
89
84
97
110
95
108
109
133
137
150
163
71
76
92
90
101
107
98
104
81
76
94
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
133
50
0
0
0
81
89
0
0
0
0
0
0
133
0
0
163
71
76
92
90
101
107
98
104
81
0
0
f
4
FINITE INTEGRAL RELATION ALGEBRAS
alg.
4643013
4673013
4703013
4733013
4763013
4793013
4823013
4853013
4883013
4913013
4943013
4973013
5003013
5033013
5063013
5093013
5123013
5153013
5183013
5213013
5243013
5273013
5303013
5333013
5363013
5393013
5423013
5453013
5483013
5513013
5543013
5573013
5603013
5633013
5663013
5693013
5723013
5753013
5783013
5813013
5843013
5873013
5903013
5933013
5963013
5993013
6023013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
13
13
15
14
15
10
13
14
13
13
15
14
15
12
14
13
15
15
15
16
12
12
14
13
14
11
13
13
11
11
13
12
13
11
13
13
13
13
15
13
14
11
13
13
q
88
106
104
99
91
115
114
124
55
100
106
98
93
114
116
126
82
106
101
128
120
137
143
62
72
84
74
100
50
62
76
60
58
76
60
76
66
92
86
88
82
108
78
96
64
86
80
b
88
106
104
99
0
0
114
124
0
100
106
98
0
114
116
126
0
106
0
128
0
137
143
0
0
0
0
0
0
0
0
0
0
0
0
0
0
92
0
0
0
0
0
0
0
0
0
f
alg.
4653013
4683013
4713013
4743013
4773013
4803013
4833013
4863013
4893013
4923013
4953013
4983013
5013013
5043013
5073013
5103013
5133013
5163013
5193013
5223013
5253013
5283013
5313013
5343013
5373013
5403013
5433013
5463013
5493013
5523013
5553013
5583013
5613013
5643013
5673013
5703013
5733013
5763013
5793013
5823013
5853013
5883013
5913013
5943013
5973013
6003013
6033013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
13
14
13
15
15
11
13
15
13
14
13
15
15
13
14
14
14
16
15
17
12
13
12
14
14
12
12
14
11
12
11
13
13
12
12
14
13
14
12
14
14
12
12
14
q
98
96
114
97
104
103
127
122
65
98
116
93
106
105
129
124
98
98
117
109
136
132
159
62
78
68
84
96
56
70
82
54
70
54
72
70
82
76
102
82
98
68
84
100
80
74
96
b
98
96
114
0
0
103
127
122
65
98
116
88
106
105
129
124
98
0
117
0
136
132
159
0
0
0
0
0
0
0
0
0
0
0
0
0
82
0
102
0
0
0
0
0
0
0
0
173
f
5
alg.
4663013
4693013
4723013
4753013
4783013
4813013
4843013
4873013
4903013
4933013
4963013
4993013
5023013
5053013
5083013
5113013
5143013
5173013
5203013
5233013
5263013
5293013
5323013
5353013
5383013
5413013
5443013
5473013
5503013
5533013
5563013
5593013
5623013
5653013
5683013
5713013
5743013
5773013
5803013
5833013
5863013
5893013
5923013
5953013
5983013
6013013
6043013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
12
14
14
14
14
16
12
14
12
14
14
14
14
16
13
15
14
15
14
16
11
13
13
13
13
15
12
13
10
12
12
12
12
14
12
13
12
14
14
13
13
15
12
13
12
q
96
106
86
110
102
116
111
135
90
108
85
106
101
118
113
137
90
114
112
125
121
148
56
68
78
78
90
106
56
76
48
66
64
66
64
82
76
92
72
98
92
74
90
106
70
90
74
b
96
106
0
110
0
116
111
135
90
108
0
106
0
118
113
137
0
114
0
125
121
148
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
92
0
0
0
0
0
0
0
0
0
f
174
alg.
6053013
6083013
6113013
6143013
6173013
6203013
6233013
6263013
6293013
6323013
6353013
6383013
6413013
6443013
6473013
6503013
6533013
6563013
6593013
6623013
6653013
6683013
6713013
6743013
6773013
6803013
6833013
6863013
6893013
6923013
6953013
6983013
7013013
7043013
7073013
7103013
7133013
7163013
7193013
7223013
7253013
7283013
7313013
7343013
7373013
7403013
7433013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
13
14
13
15
15
12
13
13
13
15
15
16
13
14
12
13
12
14
14
13
14
14
15
13
14
13
13
15
14
15
13
15
14
16
7
11
12
12
11
11
13
12
13
11
q
90
84
106
94
114
94
124
114
69
75
88
81
103
123
129
72
78
74
82
67
92
89
99
109
105
115
81
91
93
86
115
100
112
101
134
111
144
17
46
65
59
51
50
63
65
75
52
b
0
0
0
0
114
0
124
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
99
0
0
0
0
0
0
0
0
0
0
0
134
0
144
10
0
0
0
0
0
0
0
0
0
f
7
alg.
6063013
6093013
6123013
6153013
6183013
6213013
6243013
6273013
6303013
6333013
6363013
6393013
6423013
6453013
6483013
6513013
6543013
6573013
6603013
6633013
6663013
6693013
6723013
6753013
6783013
6813013
6843013
6873013
6903013
6933013
6963013
6993013
7023013
7053013
7083013
7113013
7143013
7173013
7203013
7233013
7263013
7293013
7323013
7353013
7383013
7413013
7443013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
12
14
14
14
14
16
13
14
13
14
13
14
11
12
11
13
13
13
13
15
13
15
14
16
14
15
13
14
13
15
15
14
15
15
16
9
11
10
13
11
12
11
13
13
12
q
80
100
84
114
104
114
104
134
78
84
84
94
97
103
54
60
61
86
83
79
76
101
96
125
102
131
90
100
90
102
87
116
109
121
127
131
137
31
49
47
65
50
57
59
75
71
59
b
0
0
0
114
0
114
0
134
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
121
114
131
125
0
0
0
0
0
0
0
0
0
0
f
13
12
alg.
6073013
6103013
6133013
6163013
6193013
6223013
6253013
6283013
6313013
6343013
6373013
6403013
6433013
6463013
6493013
6523013
6553013
6583013
6613013
6643013
6673013
6703013
6733013
6763013
6793013
6823013
6853013
6883013
6913013
6943013
6973013
7003013
7033013
7063013
7093013
7123013
7153013
7183013
7213013
7243013
7273013
7303013
7333013
7363013
7393013
7423013
7453013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
14
13
13
15
14
15
11
12
12
14
14
14
15
12
13
12
12
14
13
14
12
14
13
15
12
13
12
14
14
14
14
16
14
16
15
17
10
11
11
10
12
12
12
12
14
12
q
96
90
104
94
124
104
124
60
66
75
97
90
110
116
63
69
73
70
95
80
88
83
112
89
118
72
82
77
106
99
103
96
125
114
147
124
157
39
58
53
44
57
56
69
65
81
58
b
0
0
104
0
124
0
124
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
112
0
0
0
0
0
0
0
0
0
0
101
147
112
157
0
0
0
0
0
0
0
0
0
0
f
13
12
FINITE INTEGRAL RELATION ALGEBRAS
alg.
7463013
7493013
7523013
7553013
7583013
7613013
7643013
7673013
7703013
7733013
7763013
7793013
7823013
7853013
7883013
7913013
7943013
7973013
8003013
8033013
8063013
8093013
8123013
8153013
8183013
8213013
8243013
8273013
8303013
8333013
8363013
8393013
8423013
8453013
8483013
8513013
8543013
8573013
8603013
8633013
8663013
8693013
8723013
8753013
8783013
8813013
8843013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
12
13
11
13
13
13
13
15
11
13
13
12
12
14
13
14
12
14
15
10
10
11
10
12
11
13
12
13
13
12
12
14
12
13
12
14
14
12
12
14
13
13
13
15
13
14
q
65
67
76
60
77
76
87
83
103
60
82
77
82
76
102
83
99
81
111
111
44
39
60
46
65
64
87
58
63
71
68
65
83
63
69
74
96
89
66
63
82
72
89
82
105
87
89
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
102
0
0
0
111
0
0
0
0
0
0
0
87
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
alg.
7473013
7503013
7533013
7563013
7593013
7623013
7653013
7683013
7713013
7743013
7773013
7803013
7833013
7863013
7893013
7923013
7953013
7983013
8013013
8043013
8073013
8103013
8133013
8163013
8193013
8223013
8253013
8283013
8313013
8343013
8373013
8403013
8433013
8463013
8493013
8523013
8553013
8583013
8613013
8643013
8673013
8703013
8733013
8763013
8793013
8823013
8853013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
13
13
12
12
14
13
14
12
12
12
14
12
13
12
14
14
13
14
16
10
11
11
11
11
12
11
13
12
14
12
13
11
13
13
13
13
15
12
13
12
14
13
14
12
14
14
q
60
77
73
67
66
83
87
93
63
72
67
89
76
92
73
99
93
101
101
131
42
48
54
55
56
77
51
67
64
84
68
74
54
72
69
87
80
102
67
72
66
81
86
95
74
96
93
b
0
0
0
0
0
0
0
0
0
0
0
0
0
92
0
0
0
101
0
131
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
175
f
alg.
7483013
7513013
7543013
7573013
7603013
7633013
7663013
7693013
7723013
7753013
7783013
7813013
7843013
7873013
7903013
7933013
7963013
7993013
8023013
8053013
8083013
8113013
8143013
8173013
8203013
8233013
8263013
8293013
8323013
8353013
8383013
8413013
8443013
8473013
8503013
8533013
8563013
8593013
8623013
8653013
8683013
8713013
8743013
8773013
8803013
8833013
8863013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
q
12
70
12
66
14
83
12
70
13
73
12
77
14
97
14
93
13
71
12
70
13
79
11
66
13
92
13
86
13
89
13
83
15 109
13
91
15 121
9
35
11
51
10
47
12
67
11
56
12
65
12
74
12
60
12
54
13
77
11
59
13
77
13
74
12
63
12
60
14
78
13
83
14
93
11
57
13
76
13
73
13
75
12
76
14
99
14
92
13
83
13
80
15 102
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
121
0
0
0
0
0
0
58
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
16
176
alg.
8873013
8903013
8933013
8963013
8993013
9023013
9053013
9083013
9113013
9143013
9173013
9203013
9233013
9263013
9293013
9323013
9353013
9383013
9413013
9443013
9473013
9503013
9533013
9563013
9593013
9623013
9653013
9683013
9713013
9743013
9773013
9803013
9833013
9863013
9893013
9923013
9953013
9983013
10013013
10043013
10073013
10103013
10133013
10163013
10193013
10223013
10253013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
14
14
16
12
12
11
13
13
12
12
14
11
12
11
13
13
12
12
14
13
14
12
14
13
13
13
15
13
14
11
13
13
13
13
15
13
14
13
15
15
13
12
14
13
q
b
73
0
95
0
92
0
109
0
102
0
128
0
57
0
57
0
58
0
80
0
78
0
65
0
63
0
81
0
56
0
64
0
54
0
71
0
72
0
75
0
72
0
97
0
83
0
91
0
65
0
84
0
79
0
88
0
86
0
111
0
88
0
91
0
66
0
87
0
88
0
85
0
86
0
107
0
98
0
114 114
92
0
121
0
118
0
75
0
64
0
82
0
85
0
f
alg.
8883013
8913013
8943013
8973013
9003013
9033013
9063013
9093013
9123013
9153013
9183013
9213013
9243013
9273013
9303013
9333013
9363013
9393013
9423013
9453013
9483013
9513013
9543013
9573013
9603013
9633013
9663013
9693013
9723013
9753013
9783013
9813013
9843013
9873013
9903013
9933013
9963013
9993013
10023013
10053013
10083013
10113013
10143013
10173013
10203013
10233013
10263013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
14
15
11
13
12
12
12
14
12
13
10
12
12
12
12
14
12
13
12
14
14
13
12
14
13
14
12
14
14
12
12
14
13
14
12
14
14
14
14
16
13
13
12
14
q
82
79
101
109
115
50
66
61
67
65
87
65
72
47
64
65
62
63
80
76
84
70
95
92
74
70
87
89
98
75
97
95
78
79
100
82
98
85
114
111
108
105
134
73
73
72
98
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
alg.
8893013
8923013
8953013
8983013
9013013
9043013
9073013
9103013
9133013
9163013
9193013
9223013
9253013
9283013
9313013
9343013
9373013
9403013
9433013
9463013
9493013
9523013
9553013
9583013
9613013
9643013
9673013
9703013
9733013
9763013
9793013
9823013
9853013
9883013
9913013
9943013
9973013
10003013
10033013
10063013
10093013
10123013
10153013
10183013
10213013
10243013
10273013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
13
15
15
12
11
13
12
13
11
13
13
11
11
13
12
13
11
13
13
13
13
15
13
13
12
14
14
13
13
15
12
13
12
14
14
13
13
15
14
15
12
14
13
13
13
q
86
88
96
122
115
59
52
66
71
74
56
74
72
55
56
73
63
71
63
88
85
82
79
104
75
78
76
101
99
84
82
104
75
91
73
94
95
101
98
127
105
121
66
82
73
85
79
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
127
0
0
0
0
0
0
0
f
FINITE INTEGRAL RELATION ALGEBRAS
alg.
10283013
10313013
10343013
10373013
10403013
10433013
10463013
10493013
10523013
10553013
10583013
10613013
10643013
10673013
10703013
10733013
10763013
10793013
10823013
10853013
10883013
10913013
10943013
10973013
11003013
11033013
11063013
11093013
11123013
11153013
11183013
11213013
11243013
11273013
11303013
11333013
11363013
11393013
11423013
11453013
11483013
11513013
11543013
11573013
11603013
11633013
11663013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
12
14
14
12
12
14
13
14
12
14
14
14
14
16
13
14
12
14
14
13
13
15
14
15
13
15
15
13
13
15
14
15
13
15
15
15
15
17
14
13
14
13
13
15
15
11
q
92
71
89
90
70
67
88
77
89
76
105
98
102
95
124
83
92
74
95
93
98
92
121
105
118
92
114
115
95
92
117
98
118
100
133
126
130
123
156
86
72
96
84
83
101
114
56
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
121
0
113
0
0
0
0
0
0
0
117
0
133
0
130
0
156
0
0
0
0
0
0
0
0
f
alg.
10293013
10323013
10353013
10383013
10413013
10443013
10473013
10503013
10533013
10563013
10593013
10623013
10653013
10683013
10713013
10743013
10773013
10803013
10833013
10863013
10893013
10923013
10953013
10983013
5 11013013
11043013
11073013
11103013
11133013
11163013
11193013
11223013
1 11253013
11283013
11313013
11343013
11373013
11403013
11433013
11463013
11493013
11523013
11553013
11583013
11613013
11643013
11673013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
13
13
15
12
13
12
14
14
13
13
15
14
15
12
14
14
13
13
15
13
14
13
15
15
14
14
16
13
14
13
15
15
14
14
16
15
16
12
12
14
14
14
14
14
16
11
q
92
80
81
99
67
79
68
89
86
92
85
114
99
111
73
92
93
86
84
105
95
108
92
121
115
101
102
124
88
108
89
114
111
120
113
146
123
143
68
63
81
92
93
92
105
127
57
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
104
0
121
0
0
0
0
0
107
0
0
0
120
0
146
0
143
0
0
0
0
0
0
0
0
0
177
f
alg.
10303013
10333013
10363013
10393013
10423013
10453013
10483013
10513013
10543013
10573013
10603013
10633013
10663013
10693013
10723013
10753013
10783013
10813013
10843013
10873013
10903013
4 10933013
10963013
10993013
11023013
11053013
11083013
11113013
11143013
1 11173013
11203013
11233013
11263013
11293013
11323013
11353013
11383013
11413013
11443013
11473013
11503013
11533013
11563013
11593013
11623013
11653013
11683013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
13
14
11
13
13
13
13
15
13
14
13
15
15
13
13
15
13
14
12
14
14
14
14
16
14
15
12
14
14
14
14
16
14
15
14
16
16
13
13
13
15
15
14
15
10
12
q
105
80
90
58
79
76
80
77
98
89
101
86
115
108
82
83
102
83
96
82
111
105
108
102
131
105
111
79
104
101
105
102
127
113
133
110
143
136
77
72
83
105
102
92
118
48
65
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
111
0
0
0
131
0
0
0
0
0
98
0
0
0
133
0
143
0
0
0
0
0
0
0
0
0
0
f
7
178
alg.
11693013
11723013
11753013
11783013
11813013
11843013
11873013
11903013
11933013
11963013
11993013
12023013
12053013
12083013
12113013
12143013
12173013
12203013
12233013
12263013
12293013
12323013
12353013
12383013
12413013
12443013
12473013
12503013
12533013
12563013
12593013
12623013
12653013
12683013
12713013
12743013
12773013
12803013
12833013
12863013
12893013
12923013
12953013
12983013
13013013
13043013
13073013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
13
13
12
12
14
13
14
11
13
13
14
12
14
14
14
14
16
13
14
14
16
14
15
15
17
12
12
12
14
13
13
13
15
13
13
13
15
13
14
13
15
15
13
12
14
14
q
54
71
72
76
70
95
86
91
64
85
83
94
82
111
105
107
101
130
96
105
109
131
116
133
129
159
60
71
68
87
72
91
84
107
73
85
82
103
78
90
91
116
109
73
71
93
90
b
0
0
0
0
0
0
0
0
0
0
0
0
0
111
0
0
0
129
0
0
0
0
0
133
0
159
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
alg.
11703013
11733013
11763013
11793013
11823013
11853013
11883013
11913013
11943013
11973013
12003013
12033013
12063013
12093013
12123013
12153013
12183013
1 12213013
12243013
12273013
12303013
12333013
12363013
12393013
12423013
12453013
12483013
12513013
12543013
12573013
12603013
12633013
12663013
12693013
12723013
12753013
12783013
12813013
12843013
12873013
12903013
12933013
12963013
12993013
13023013
13053013
13083013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
12
14
12
13
12
14
14
12
12
14
14
13
13
15
14
15
12
14
14
15
13
15
15
16
11
13
12
13
12
14
13
14
12
14
13
14
12
14
14
14
14
16
13
13
13
15
q
b
62
0
66
0
80
0
77
0
82
0
73
0
98
0
92
0
76
0
74
0
95
0
92
0
98
96
92
0
121 121
104
0
117
0
83
0
112
0
102
0
125
0
103
0
136 136
126
0
149 149
51
0
69
0
66
0
80
0
63
0
84
0
82
0
100
0
64
0
82
0
82
0
94
0
69
0
90
0
87
0
107
0
100
0
125
0
73
0
83
0
80
0
102
0
f
alg.
11713013
11743013
11773013
11803013
11833013
11863013
11893013
11923013
11953013
11983013
12013013
12043013
2 12073013
12103013
12133013
12163013
12193013
12223013
12253013
12283013
12313013
12343013
12373013
12403013
12433013
12463013
12493013
12523013
12553013
12583013
12613013
12643013
12673013
12703013
12733013
12763013
12793013
12823013
12853013
12883013
12913013
12943013
12973013
13003013
13033013
13063013
13093013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
13
11
13
13
13
13
15
12
13
13
15
13
14
13
15
15
13
13
15
15
14
14
16
16
12
11
13
13
13
12
14
14
13
12
14
14
13
13
15
14
15
12
14
13
14
13
q
63
74
64
89
83
85
79
104
73
86
82
104
95
108
91
120
114
99
89
118
115
123
113
146
139
60
59
78
75
75
75
98
91
73
73
94
91
81
78
99
100
116
64
82
81
92
81
b
0
0
0
0
0
0
0
0
0
0
0
0
0
106
0
119
0
0
0
0
0
123
0
146
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
2
1
FINITE INTEGRAL RELATION ALGEBRAS
alg.
13103013
13133013
13163013
13193013
13223013
13253013
13283013
13313013
13343013
13373013
13403013
13433013
13463013
13493013
13523013
13553013
13583013
13613013
13643013
13673013
13703013
13733013
13763013
13793013
13823013
13853013
13883013
13913013
13943013
13973013
14003013
14033013
14063013
14093013
14123013
14153013
14183013
14213013
14243013
14273013
14303013
14333013
14363013
14393013
14423013
14453013
14483013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
13
15
15
14
13
15
15
14
14
16
15
16
11
13
12
13
11
13
13
12
12
14
13
14
12
14
13
14
11
13
13
13
13
15
13
14
13
15
15
12
12
14
12
13
12
14
q
93
93
119
112
90
88
113
110
100
97
122
126
138
48
66
62
76
58
75
79
75
73
98
91
91
60
78
77
89
60
80
81
77
78
98
94
99
87
115
112
64
68
82
74
80
71
91
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
f
alg.
13113013
13143013
13173013
13203013
13233013
13263013
13293013
13323013
13353013
13383013
13413013
13443013
13473013
13503013
13533013
13563013
13593013
13623013
13653013
13683013
13713013
13743013
13773013
13803013
13833013
13863013
13893013
13923013
13953013
13983013
14013013
14043013
14073013
14103013
14133013
14163013
14193013
14223013
14253013
14283013
14313013
14343013
14373013
14403013
8 14433013
14463013
14493013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
14
14
16
14
14
14
16
14
15
14
16
16
12
11
13
13
12
12
14
12
13
12
14
14
13
12
14
14
12
12
14
13
14
12
14
14
14
14
16
12
13
11
13
13
13
13
q
b
90
0
109
0
102
0
128 126
90
0
100
0
97
0
122
0
101
0
109
0
113
0
142
0
135
0
57
0
55
0
74
0
71
0
63
0
67
0
84
0
82
0
82
0
75
0
100
0
98
0
69
0
68
0
89
0
86
0
68
0
69
0
89
0
81
0
86
0
78
0
106
0
103
0
99
0
96
0
124
0
68
0
73
0
62
0
82
0
84
0
79
0
81
0
179
f
alg.
13123013
13153013
13183013
2 13213013
13243013
13273013
13303013
13333013
13363013
13393013
13423013
13453013
13483013
13513013
13543013
13573013
13603013
13633013
13663013
13693013
13723013
13753013
13783013
13813013
13843013
13873013
13903013
13933013
13963013
13993013
14023013
14053013
14083013
14113013
14143013
14173013
14203013
14233013
14263013
14293013
14323013
14353013
14383013
14413013
14443013
14473013
14503013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
14
15
13
15
14
15
13
15
15
15
15
17
12
12
12
14
12
13
11
13
13
13
13
15
13
13
13
15
12
13
12
14
14
13
13
15
14
15
11
13
13
12
12
14
13
14
q
b f
102
0
103
0
118 116 2
81
0
99
0
101
0
109
0
88
0
113
0
110
0
129
0
122
0
151
0
57
0
67
0
64
0
83
0
70
0
72
0
66
0
91
0
89
0
84
0
82
0
107
0
69
0
80
0
77
0
98
0
72
0
77
0
69
0
89
0
90
0
90
0
87
0
115
0
103
0
108
0
59
0
73
0
77
0
70
0
72
0
92
76 16
83
0
89
0
180
alg.
14513013
14543013
14573013
14603013
14633013
14663013
14693013
14723013
14753013
14783013
14813013
14843013
14873013
14903013
14933013
14963013
14993013
15023013
15053013
15083013
15113013
15143013
15173013
15203013
15233013
15263013
15293013
15323013
15353013
15383013
15413013
15443013
15473013
15503013
15533013
15563013
15593013
15623013
15653013
15683013
15713013
15743013
15773013
15803013
15833013
15863013
15893013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
13
13
15
13
14
13
15
15
13
13
15
13
14
13
15
15
13
13
15
14
15
13
15
15
15
15
17
13
13
13
15
13
14
12
14
14
14
14
16
14
14
14
16
13
14
13
q
b
93
0
84
0
85
0
105
0
100
0
106 97
93
0
121 120
119
0
81
0
81
0
99
0
87
0
100
0
84
0
108
0
109
0
91
0
92
0
116
0
100
0
113
0
100
0
132 132
129
0
125
0
122
0
154 153
76
0
85
0
86
0
105
0
84
0
94
0
83
0
112
0
106
0
109
0
103
0
132
0
90
0
100
0
101
0
122
0
88
0
97
0
89
0
f
alg.
14523013
14553013
14583013
14613013
14643013
9 14673013
14703013
1 14733013
14763013
14793013
14823013
14853013
14883013
14913013
14943013
14973013
15003013
15033013
15063013
15093013
15123013
15153013
15183013
15213013
15243013
15273013
15303013
1 15333013
15363013
15393013
15423013
15453013
15483013
15513013
15543013
15573013
15603013
15633013
15663013
15693013
15723013
15753013
15783013
15813013
15843013
15873013
15903013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
13
14
12
14
14
14
14
16
13
14
12
14
14
14
14
16
13
14
13
15
15
14
14
16
15
16
12
14
13
14
12
14
14
13
13
15
14
15
13
15
14
15
12
14
14
14
q
101
88
93
84
112
110
105
103
131
81
90
75
99
100
96
97
121
91
104
88
112
113
116
113
145
125
138
63
85
80
98
72
93
97
96
90
119
112
116
77
99
97
113
76
100
97
101
b
0
0
0
0
112
102
0
0
130
0
0
0
0
0
0
0
0
0
0
0
0
0
114
0
145
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
alg.
14533013
14563013
14593013
14623013
14653013
8 14683013
14713013
14743013
1 14773013
14803013
14833013
14863013
14893013
14923013
14953013
14983013
15013013
15043013
15073013
15103013
15133013
15163013
2 15193013
15223013
15253013
15283013
15313013
15343013
15373013
15403013
15433013
15463013
15493013
15523013
15553013
15583013
15613013
15643013
15673013
15703013
15733013
15763013
15793013
15823013
15853013
15883013
15913013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
13
13
15
14
15
12
14
14
13
13
15
14
15
12
14
14
14
14
16
14
15
14
16
16
13
12
14
14
13
13
15
13
14
13
15
15
14
13
15
15
13
13
15
14
q
b
76
0
96
0
97
0
96
0
94
0
122 122
109
0
115
0
72
0
90
0
90
0
87
0
88
0
112
0
96
0
109
0
79
0
103
0
104
0
100
0
101
0
125
0
116
0
129 127
109
0
141 140
138
0
72
0
73
0
92
0
93
0
81
0
85
0
106
0
99
0
103
0
96
0
125
0
119
0
86
0
88
0
109
0
110
0
88
0
85
0
109
0
101
0
f
2
1
FINITE INTEGRAL RELATION ALGEBRAS
alg.
15923013
15953013
15983013
16013013
16043013
16073013
16103013
16133013
16163013
16193013
16223013
16253013
16283013
16313013
16343013
16373013
16403013
16433013
16463013
16493013
16523013
16553013
16583013
16613013
16643013
16673013
16703013
16733013
16763013
16793013
16823013
16853013
16883013
16913013
16943013
16973013
17003013
17033013
17063013
17093013
17123013
17153013
17183013
17213013
17243013
17273013
17303013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
15
14
14
16
15
16
12
14
14
13
13
15
14
15
13
15
15
14
14
16
15
16
13
15
15
14
14
16
15
16
13
15
15
15
15
17
15
16
15
17
17
11
11
13
11
13
q
113
110
113
106
138
126
135
72
90
94
90
88
112
103
113
92
116
117
119
113
145
132
142
87
109
109
109
106
134
118
135
97
125
122
126
123
151
137
154
134
170
163
53
56
77
54
75
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
106
0
0
0
0
0
145
130
136
0
0
0
0
0
0
0
0
0
125
110
119
0
151
123
154
121
170
151
0
0
0
0
0
f
7
2
6
12
7
14
13
12
alg.
15933013
15963013
15993013
16023013
16053013
16083013
16113013
16143013
16173013
16203013
16233013
16263013
16293013
16323013
16353013
16383013
16413013
16443013
16473013
16503013
16533013
16563013
16593013
16623013
16653013
16683013
16713013
16743013
16773013
16803013
16833013
16863013
16893013
16923013
16953013
16983013
17013013
17043013
17073013
17103013
17133013
17163013
17193013
17223013
17253013
17283013
17313013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
16
14
15
14
16
16
13
13
15
13
14
13
15
15
14
14
16
14
15
14
16
16
14
14
16
14
15
14
16
16
14
14
16
15
16
14
16
16
16
16
18
12
12
13
12
13
q
98
122
113
122
110
142
135
81
85
103
90
100
91
115
113
104
105
129
119
129
116
148
142
100
100
122
105
122
106
134
131
113
110
138
122
139
121
157
150
154
147
183
62
68
74
66
72
b f
alg.
0
15943013
0
15973013
0
16003013
0
16033013
0
16063013
0
16093013
0
16123013
0
16153013
0
16183013
0
16213013
0
16243013
0
16273013
0
16303013
0
16333013
0
16363013
0
16393013
0
16423013
0
16453013
114
5 16483013
124
5 16513013
0
16543013
148
16573013
140
2 16603013
0
16633013
0
16663013
0
16693013
0
16723013
0
16753013
0
16783013
0
16813013
0
16843013
0
16873013
0
16903013
138
16933013
0
16963013
138
1 16993013
106 15 17023013
157
17053013
136 14 17083013
154
17113013
135 12 17143013
183
17173013
0
17203013
0
17233013
0
17263013
0
17293013
0
17323013
181
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
13
15
15
15
15
17
13
14
12
14
14
14
14
16
14
15
13
15
15
15
15
17
14
15
13
15
15
15
15
17
14
15
14
16
16
15
15
17
16
17
10
13
12
14
12
14
q
110
97
129
122
126
119
151
81
94
78
102
100
103
101
125
104
117
103
135
129
132
126
158
96
113
93
121
118
122
119
147
109
126
110
138
135
141
134
170
150
167
44
71
65
86
63
84
b f
0
0
0
0
0
0
0
0
0
0
0
0
0
0
116
9
0
0
0
135
124
5
0
0
158
0
0
0
0
0
0
0
0
0
123
3
0
138
124 11
141
120 14
170
138 12
167
0
0
0
0
0
0
182
alg.
17333013
17363013
17393013
17423013
17453013
17483013
17513013
17543013
17573013
17603013
17633013
17663013
17693013
17723013
17753013
17783013
17813013
17843013
17873013
17903013
17933013
17963013
17993013
18023013
18053013
18083013
18113013
18143013
18173013
18203013
18233013
18263013
18293013
18323013
18353013
18383013
18413013
18443013
18473013
18503013
18533013
18563013
18593013
18623013
18653013
18683013
18713013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
12
13
12
14
14
14
14
16
12
14
13
15
13
14
13
15
15
14
15
15
16
14
13
15
14
16
12
14
13
15
13
15
15
15
15
17
15
17
16
18
13
15
13
15
15
q
70
95
71
80
68
92
89
103
96
124
76
93
85
102
95
100
88
113
116
110
129
119
138
101
85
109
107
135
77
97
89
109
95
123
123
119
119
147
132
164
144
176
93
113
99
127
127
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
101
0
0
101
135
0
0
0
0
0
121
123
117
0
147
0
164
0
176
0
0
0
123
122
f
6
2
2
4
5
alg.
17343013
17373013
17403013
17433013
17463013
17493013
17523013
17553013
17583013
17613013
17643013
17673013
17703013
17733013
17763013
17793013
17823013
17853013
17883013
17913013
17943013
17973013
18003013
18033013
18063013
18093013
18123013
18153013
18183013
18213013
18243013
18273013
18303013
18333013
18363013
18393013
18423013
18453013
18483013
18513013
18543013
18573013
18603013
18633013
18663013
18693013
18723013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
13
14
13
13
15
14
15
11
13
12
14
12
14
14
14
14
16
14
16
15
17
15
14
15
15
16
13
14
14
15
14
14
16
15
16
14
16
15
17
12
14
15
14
14
16
q
86
88
83
92
80
77
101
99
112
64
81
73
90
79
104
107
97
100
125
113
142
122
151
113
97
109
123
131
85
101
97
113
107
107
135
123
131
116
148
128
160
81
101
117
111
111
139
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
113
0
0
123
125
0
0
0
0
103
0
135
0
131
0
148
0
160
0
0
117
0
0
136
f
alg.
17353013
17383013
17413013
17443013
17473013
17503013
17533013
17563013
17593013
17623013
17653013
17683013
17713013
17743013
17773013
17803013
17833013
17863013
17893013
17923013
17953013
17983013
18013013
18043013
18073013
18103013
18133013
6 18163013
18193013
18223013
18253013
18283013
4 18313013
18343013
18373013
18403013
18433013
18463013
18493013
18523013
18553013
18583013
18613013
18643013
18673013
18703013
3 18733013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
15
14
15
13
14
13
15
15
12
13
13
14
13
13
15
14
15
13
15
14
16
13
16
14
16
15
17
13
15
14
16
14
15
14
16
16
15
16
16
17
13
14
16
14
15
15
q
79
104
95
104
80
89
87
115
108
69
88
78
97
88
91
116
104
109
97
126
106
135
89
125
97
121
119
147
89
109
101
121
111
119
107
135
135
132
148
144
160
89
105
125
115
123
123
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
89
125
0
0
113
147
0
109
0
121
0
119
0
135
135
132
148
144
160
0
0
125
111
0
123
f
6
4
FINITE INTEGRAL RELATION ALGEBRAS
alg.
18743013
18773013
18803013
18833013
18863013
18893013
18923013
18953013
18983013
19013013
19043013
19073013
19103013
19133013
19163013
19193013
19223013
19253013
19283013
19313013
19343013
19373013
19403013
19433013
19463013
19493013
19523013
19553013
19583013
19613013
19643013
19673013
19703013
19733013
19763013
19793013
19823013
19853013
19883013
19913013
19943013
19973013
20003013
20033013
20063013
20093013
20123013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
16
14
16
15
17
15
17
18
11
10
12
10
11
10
12
10
12
13
11
11
10
11
13
11
13
11
11
13
10
12
12
12
12
14
11
13
11
12
11
13
12
12
12
14
12
14
11
q
135
120
152
132
164
144
180
192
48
44
62
44
60
54
77
62
89
83
49
46
49
63
85
55
77
56
61
76
55
76
67
87
74
99
56
78
56
71
63
78
72
85
78
104
71
95
60
b f
alg.
135
18753013
116 4 18783013
150 2 18813013
132
18843013
164
18873013
144
18903013
180
18933013
192
18963013
0
18993013
0
19023013
0
19053013
0
19083013
60
19113013
0
19143013
77
19173013
0
19203013
89
19233013
0
19263013
0
19293013
0
19323013
37 12 19353013
50 13 19383013
0
19413013
0
19443013
0
19473013
0
19503013
0
19533013
0
19563013
0
19593013
0
19623013
0
19653013
0
19683013
0
19713013
0
19743013
0
19773013
0
19803013
0
19833013
0
19863013
0
19893013
0
19923013
0
19953013
85
19983013
0
20013013
104
20043013
0
20073013
0
20103013
0
20133013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
16
15
16
16
17
16
17
19
11
11
12
11
11
11
12
11
12
14
11
11
11
12
11
12
12
11
12
12
11
11
13
12
13
11
12
11
12
12
12
11
13
12
13
12
13
12
12
q
139
136
152
148
164
164
176
212
46
47
76
52
55
70
68
82
76
103
59
55
58
76
56
60
57
51
73
68
67
58
79
80
90
54
61
52
64
69
69
63
84
79
94
69
76
67
72
b
139
132
152
148
164
164
176
212
0
0
0
52
0
70
0
82
0
103
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
84
0
94
0
0
0
0
183
f
alg.
18763013
4 18793013
18823013
18853013
18883013
18913013
18943013
18973013
19003013
19033013
19063013
19093013
19123013
19153013
19183013
19213013
19243013
19273013
19303013
19333013
19363013
19393013
19423013
19453013
19483013
19513013
19543013
19573013
19603013
19633013
19663013
19693013
19723013
19753013
19783013
19813013
19843013
19873013
19903013
19933013
19963013
19993013
20023013
20053013
20083013
20113013
20143013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
17
15
17
16
18
16
18
8
12
11
13
10
12
11
13
11
13
10
12
12
12
12
12
12
10
12
12
13
11
12
11
13
13
12
12
12
11
13
12
12
11
13
13
13
13
13
12
q
151
136
168
148
180
160
196
18
61
59
79
48
67
61
84
69
96
44
64
64
67
72
61
72
48
59
64
77
64
70
71
96
83
59
73
58
59
81
72
75
69
95
88
74
90
73
67
b f
151
134 2
168
148
180
160
196
10 8
0
0
0
0
67
0
84
0
96
0
0
0
48 19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
95
0
0
0
0
0
184
alg.
20153013
20183013
20213013
20243013
20273013
20303013
20333013
20363013
20393013
20423013
20453013
20483013
20513013
20543013
20573013
20603013
20633013
20663013
20693013
20723013
20753013
20783013
20813013
20843013
20873013
20903013
20933013
20963013
20993013
21023013
21053013
21083013
21113013
21143013
21173013
21203013
21233013
21263013
21293013
21323013
21353013
21383013
21413013
21443013
21473013
21503013
21533013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
12
13
12
14
12
13
11
13
13
13
13
15
13
12
13
13
12
11
13
13
12
13
13
14
12
13
13
13
13
13
14
13
14
14
13
12
14
14
13
14
14
15
12
13
13
12
q
79
75
88
80
95
78
92
77
107
96
104
93
123
97
70
75
85
71
69
94
85
95
105
98
108
68
76
86
79
90
103
113
83
91
103
87
83
112
103
115
121
122
128
71
90
72
67
b
0
0
0
0
0
0
92
0
107
0
104
0
123
91
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
103
0
0
0
0
0
0
0
0
115
0
122
0
0
0
0
0
f
alg.
20163013
20193013
20223013
20253013
20283013
20313013
20343013
20373013
20403013
20433013
20463013
20493013
20523013
6 20553013
20583013
20613013
20643013
20673013
20703013
20733013
20763013
20793013
20823013
20853013
20883013
20913013
20943013
20973013
21003013
21033013
21063013
21093013
21123013
21153013
21183013
21213013
21243013
21273013
21303013
21333013
21363013
21393013
21423013
21453013
21483013
21513013
21543013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
11
13
13
13
11
13
13
12
12
14
13
14
11
14
13
12
14
12
12
12
14
12
14
13
15
13
12
14
12
14
13
15
14
13
15
13
13
13
15
13
15
14
16
13
14
11
13
q
65
91
82
86
69
94
85
97
86
116
94
113
71
110
79
76
98
66
81
72
97
92
121
95
124
77
77
99
77
102
100
129
92
94
116
82
99
90
119
108
141
115
148
76
95
62
75
b
0
0
0
0
0
94
0
97
0
116
0
113
0
106
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
129
0
0
0
0
0
0
0
0
141
0
148
0
0
0
0
f
alg.
20173013
20203013
20233013
20263013
20293013
20323013
20353013
20383013
20413013
20443013
20473013
20503013
20533013
4 20563013
20593013
20623013
20653013
20683013
20713013
20743013
20773013
20803013
20833013
20863013
20893013
20923013
20953013
20983013
21013013
21043013
21073013
21103013
21133013
21163013
21193013
21223013
21253013
21283013
21313013
21343013
21373013
21403013
21433013
21463013
21493013
21523013
21553013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
12
14
13
12
12
14
12
13
12
14
14
12
11
12
13
11
13
12
13
11
13
12
14
11
12
13
12
13
12
14
12
13
14
12
14
13
14
12
14
13
15
11
12
12
12
12
q
81
72
98
89
85
76
101
87
106
84
114
103
84
61
66
89
63
74
82
84
79
108
82
111
59
67
90
71
89
87
116
74
82
107
75
94
96
106
95
128
102
135
66
85
67
70
77
b f
0
0
0
0
85
0
101
0
106
0
114
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
80
9
0
116
0
0
0
0
0
0
96 10
0
128
0
135
0
0
0
0
0
FINITE INTEGRAL RELATION ALGEBRAS
alg.
21563013
21593013
21623013
21653013
21683013
21713013
21743013
21773013
21803013
21833013
21863013
21893013
21923013
21953013
21983013
22013013
22043013
22073013
22103013
22133013
22163013
22193013
22223013
22253013
22283013
22313013
22343013
22373013
22403013
22433013
22463013
22493013
22523013
22553013
22583013
22613013
22643013
22673013
22703013
22733013
22763013
22793013
22823013
22853013
22883013
22913013
22943013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
12
14
12
13
12
14
14
13
12
14
13
13
12
14
14
13
14
13
14
13
13
15
15
12
11
12
12
14
13
13
13
15
12
11
12
12
11
13
11
13
13
13
12
14
12
13
q
b
89
0
78
0
92
0
78
0
86
0
87
0
112
0
101
0
71
0
72
0
97
0
82
0
89
0
82
0
111
0
104
0
95
0
104
0
102 102
104
0
114 114
103
0
136 136
125
0
69
0
67
0
72
0
78
0
91
0
79
0
99
0
88
0
116
0
63
0
69
0
75
0
69
0
59
0
73
0
69
0
93
93
87
0
84
0
72
0
94
0
87
0
101
0
f
alg.
21573013
21603013
21633013
21663013
21693013
21723013
21753013
21783013
21813013
21843013
21873013
21903013
21933013
21963013
21993013
22023013
22053013
22083013
22113013
22143013
22173013
22203013
22233013
22263013
22293013
22323013
22353013
22383013
22413013
22443013
22473013
22503013
22533013
22563013
22593013
22623013
22653013
22683013
22713013
22743013
22773013
22803013
22833013
22863013
22893013
22923013
22953013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
11
13
13
13
13
15
12
13
12
14
13
13
13
15
13
15
13
15
13
14
14
16
12
12
13
13
12
14
13
14
11
13
12
12
13
12
12
12
12
14
13
13
11
13
13
q
82
87
69
90
83
103
92
117
70
84
73
91
86
98
91
120
95
113
95
120
107
123
112
145
66
79
84
86
74
91
95
104
57
71
81
75
81
67
69
81
75
99
82
84
75
103
97
b f
alg.
0
21583013
0
21613013
0
21643013
0
21673013
0
21703013
0
21733013
0
21763013
0
21793013
0
21823013
0
21853013
0
21883013
0
21913013
0
21943013
0
21973013
0
22003013
0
22033013
0
22063013
0
22093013
0
22123013
120
22153013
94 13 22183013
123
22213013
0
22243013
145
22273013
0
22303013
0
22333013
0
22363013
0
22393013
0
22423013
0
22453013
0
22483013
0
22513013
0
22543013
0
22573013
81
22603013
0
22633013
0
22663013
0
22693013
0
22723013
0
22753013
0
22783013
0
22813013
0
22843013
0
22873013
0
22903013
103
22933013
0
22963013
185
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
13
12
12
14
13
14
12
13
13
13
12
14
13
14
12
14
12
14
12
14
14
15
11
13
13
14
13
13
12
14
14
12
10
11
13
14
12
13
12
13
12
14
13
12
12
14
q
b f
94
0
83
0
81
0
74
0
95
0
96
0
108
0
62
0
78
0
85
0
82
0
77
0
98
0
95
0
107
0
86
0
104
0
86
68 18
111 111
94
0
127 127
116
0
132 132
61
0
74
0
91
0
96
0
83
0
86
0
83
0
111
0
100
0
65
0
57
0
63
0
87
0
93
0
65
0
77
0
81
80
1
87
0
76
0
90
0
82
0
91
0
85
0
113 113
186
alg.
22973013
23003013
23033013
23063013
23093013
23123013
23153013
23183013
23213013
23243013
23273013
23303013
23333013
23363013
23393013
23423013
23453013
23483013
23513013
23543013
23573013
23603013
23633013
23663013
23693013
23723013
23753013
23783013
23813013
23843013
23873013
23903013
23933013
23963013
23993013
24023013
24053013
24083013
24113013
24143013
24173013
24203013
24233013
24263013
24293013
24323013
24353013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
13
11
13
13
12
12
14
13
14
12
14
13
13
13
15
14
13
13
15
13
14
13
15
15
13
13
15
14
15
15
16
13
14
13
14
12
14
14
14
12
14
14
14
14
q
81
109
103
82
64
82
79
89
79
107
94
104
76
93
85
101
94
122
104
97
90
116
105
123
102
134
124
96
89
114
125
138
130
143
78
94
101
103
82
107
101
104
95
127
124
117
114
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
101
0
122
0
0
0
0
0
123
0
134
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
127
122
0
0
f
alg.
22983013
23013013
23043013
23073013
23103013
23133013
23163013
23193013
23223013
23253013
23283013
23313013
23343013
23373013
23403013
23433013
23463013
23493013
23523013
23553013
23583013
23613013
23643013
23673013
23703013
23733013
23763013
23793013
23823013
23853013
23883013
23913013
23943013
23973013
24003013
24033013
24063013
24093013
24123013
24153013
24183013
24213013
24243013
24273013
2 24303013
24333013
24363013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
13
12
12
14
12
13
12
14
14
13
12
14
13
14
13
15
13
14
12
14
14
14
14
16
13
14
12
13
13
14
12
14
12
14
14
13
13
15
14
13
13
15
14
15
q
97
91
119
83
76
73
91
85
95
82
110
100
84
76
97
97
110
95
112
91
106
93
125
115
122
112
144
97
101
93
106
98
111
72
90
85
113
107
94
88
113
105
111
108
140
117
130
b
0
0
0
0
0
0
0
0
0
0
108
0
0
0
0
0
110
0
0
0
0
0
125
0
122
0
144
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
140
0
0
f
alg.
22993013
23023013
23053013
23083013
23113013
23143013
23173013
23203013
23233013
23263013
2 23293013
23323013
23353013
23383013
23413013
23443013
23473013
23503013
23533013
23563013
23593013
23623013
23653013
23683013
23713013
23743013
23773013
23803013
23833013
23863013
23893013
23923013
23953013
23983013
24013013
24043013
24073013
24103013
24133013
24163013
24193013
24223013
24253013
24283013
24313013
24343013
24373013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
14
12
14
12
13
11
13
13
13
13
15
13
13
12
14
14
14
12
14
14
13
13
15
14
15
12
14
14
13
14
14
15
13
13
13
13
15
13
14
13
15
13
14
13
15
15
q
93
107
74
91
70
85
73
101
91
98
88
116
85
88
85
113
106
103
81
107
100
113
103
135
114
132
84
109
102
109
122
114
127
84
86
97
91
119
95
100
92
117
111
124
101
133
130
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
113
0
0
0
0
0
113
0
135
0
132
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
f
FINITE INTEGRAL RELATION ALGEBRAS
alg.
24383013
24413013
24443013
24473013
24503013
24533013
24563013
24593013
24623013
24653013
24683013
24713013
24743013
24773013
24803013
24833013
24863013
24893013
24923013
24953013
24983013
25013013
25043013
25073013
25103013
25133013
25163013
25193013
25223013
25253013
25283013
25313013
25343013
25373013
25403013
25433013
25463013
25493013
25523013
25553013
25583013
25613013
25643013
25673013
25703013
25733013
25763013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
16
13
14
12
13
15
16
14
14
13
15
15
14
14
16
14
15
13
15
15
15
15
17
12
13
13
12
14
14
15
13
15
13
14
14
16
14
14
15
14
12
13
15
16
15
14
14
q
146
90
102
89
98
130
139
98
105
101
133
126
113
110
135
114
126
113
149
142
142
135
171
81
88
86
87
115
109
115
89
115
107
125
115
147
107
123
136
103
93
103
135
145
126
115
109
b f
alg.
0
24393013
0
24423013
0
24453013
0
24483013
0
24513013
0
24543013
0
24573013
0
24603013
0
24633013
0
24663013
132 1 24693013
0
24723013
0
24753013
0
24783013
0
24813013
0
24843013
0
24873013
0
24903013
149
24933013
130 12 24963013
142
24993013
0
25023013
171
25053013
81
25083013
0
25113013
0
25143013
0
25173013
115
25203013
96 13 25233013
0
25263013
0
25293013
113 2 25323013
0
25353013
125
25383013
0
25413013
147
25443013
107
25473013
123
25503013
136
25533013
0
25563013
0
25593013
0
25623013
135
25653013
145
25683013
0
25713013
0
25743013
0
25773013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
12
14
14
13
14
14
13
15
14
14
14
16
14
15
13
15
15
14
14
16
15
16
12
13
14
13
13
13
15
12
14
12
14
14
15
13
15
15
16
14
13
14
14
14
16
14
15
q
81
102
99
105
114
107
89
110
102
117
110
142
114
122
101
130
123
133
126
162
138
155
71
93
96
84
103
97
125
79
105
95
127
117
135
94
119
139
152
101
109
119
113
113
138
112
125
b f
alg.
0
24403013
0
24433013
0
24463013
0
24493013
0
24523013
0
24553013
0
24583013
0
24613013
0
24643013
0
24673013
0
24703013
141
1 24733013
0
24763013
0
24793013
0
24823013
127
3 24853013
0
24883013
133
24913013
0
24943013
162
24973013
0
25003013
155
25033013
71
25063013
93
25093013
0
25123013
0
25153013
103
25183013
0
25213013
125
25243013
0
25273013
0
25303013
0
25333013
127
25363013
0
25393013
135
25423013
85
9 25453013
119
25483013
139
25513013
152
25543013
0
25573013
0
25603013
106 13 25633013
0
25663013
0
25693013
0
25723013
0
25753013
118
7 25783013
187
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
13
15
14
14
15
14
13
15
14
15
13
15
15
14
14
16
14
15
14
16
16
13
14
12
14
13
14
14
13
14
13
13
15
15
14
13
14
13
15
14
14
15
15
13
15
15
q
93
90
111
121
114
123
101
93
114
117
126
101
126
123
117
110
139
129
146
122
158
151
79
105
74
96
99
113
107
95
99
115
105
137
127
106
107
120
91
113
125
119
129
125
99
128
122
b f
0
0
0
0
0
0
0
0
0
107 10
0
0
0
0
0
0
136
3
0
146
0
158
0
79
105
0
0
0
113
0
0
0
115
0
137
115 12
100
6
0
0
0
0
125
0
116 13
0
0
0
0
188
alg.
25793013
25823013
25853013
25883013
25913013
25943013
25973013
26003013
26033013
26063013
26093013
26123013
26153013
26183013
26213013
26243013
26273013
26303013
26333013
26363013
26393013
26423013
26453013
26483013
26513013
26543013
26573013
26603013
26633013
26663013
26693013
26723013
26753013
26783013
26813013
26843013
26873013
26903013
26933013
26963013
26993013
27023013
27053013
27083013
27113013
27143013
27173013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
16
14
15
14
16
16
15
16
15
16
17
13
13
15
13
15
14
15
14
15
11
13
13
12
12
14
14
13
13
15
12
13
12
14
14
13
13
15
13
14
13
15
15
14
14
16
13
q
138
131
148
125
161
154
137
147
157
170
183
87
98
114
94
114
109
117
115
127
63
80
79
75
82
102
98
93
89
114
78
93
77
98
98
97
93
117
103
118
98
127
123
119
115
139
90
b f
alg.
137 1 25803013
0
25833013
148
25863013
0
25893013
161
25923013
147 7 25953013
127 10 25983013
147
26013013
157
26043013
170
26073013
183
26103013
0
26133013
0
26163013
0
26193013
0
26223013
0
26253013
109
26283013
117
26313013
0
26343013
115 12 26373013
0
26403013
0
26433013
0
26463013
0
26493013
0
26523013
0
26553013
0
26583013
0
26613013
0
26643013
0
26673013
0
26703013
0
26733013
0
26763013
0
26793013
0
26823013
0
26853013
73 20 26883013
117
26913013
0
26943013
0
26973013
0
27003013
127
27033013
117 6 27063013
0
27093013
0
27123013
0
27153013
0
27183013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
13
15
15
15
15
17
15
17
16
17
18
13
14
13
14
12
13
13
15
15
12
12
14
13
13
13
15
13
14
11
13
13
13
13
15
13
14
12
14
14
14
14
16
14
15
12
14
q
115
151
144
145
138
174
134
163
177
190
203
87
106
84
106
85
93
103
131
123
72
71
88
83
94
90
110
94
101
69
90
90
89
89
110
97
105
90
119
115
114
110
139
111
131
81
102
b
0
151
0
145
0
174
125
163
177
190
203
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
105
0
0
0
114
0
139
0
0
0
0
f
alg.
25813013
25843013
25873013
25903013
25933013
25963013
9 25993013
26023013
26053013
26083013
26113013
26143013
26173013
26203013
26233013
26263013
26293013
26323013
26353013
26383013
26413013
26443013
26473013
26503013
26533013
26563013
26593013
26623013
26653013
26683013
26713013
26743013
26773013
26803013
26833013
26863013
26893013
26923013
26953013
26983013
27013013
27043013
27073013
27103013
27133013
27163013
27193013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
14
16
15
16
14
16
14
15
16
12
14
14
14
14
13
14
14
14
16
12
13
11
14
13
14
12
14
14
12
12
14
13
14
12
14
14
13
13
15
14
15
13
15
15
13
13
q
135
128
164
141
158
121
150
137
150
163
79
95
106
92
102
97
105
119
111
139
71
80
67
91
90
102
81
106
102
81
81
102
86
101
85
109
105
106
102
131
111
126
103
127
123
93
93
b f
135
0
164
134 7
158
108 13
144 6
0
0
0
0
0
0
0
0
0
0
0
0
136
3
0
0
0
91
0
0
0
0
0
0
0
0
0
101
0
0
105
0
0
0
0
126
0
0
0
0
0
FINITE INTEGRAL RELATION ALGEBRAS
alg.
27203013
27233013
27263013
27293013
27323013
27353013
27383013
27413013
27443013
27473013
27503013
27533013
27563013
27593013
27623013
27653013
27683013
27713013
27743013
27773013
27803013
27833013
27863013
27893013
27923013
27953013
27983013
28013013
28043013
28073013
28103013
28133013
28163013
28193013
28223013
28253013
28283013
28313013
28343013
28373013
28403013
28433013
28463013
28493013
28523013
28553013
28583013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
13
13
15
15
13
13
15
14
15
13
15
15
14
14
16
15
16
13
16
16
12
13
13
14
13
13
15
14
15
13
15
14
16
12
14
13
15
13
15
15
14
14
16
15
16
14
q
105
97
102
131
127
106
102
127
111
130
106
134
130
134
126
159
139
158
112
160
152
78
93
86
101
99
99
127
111
119
112
144
120
152
87
112
99
124
100
124
124
124
120
152
136
148
116
b f
alg.
0
27213013
0
27243013
0
27273013
0
27303013
0
27333013
0
27363013
0
27393013
0
27423013
0
27453013
130
27483013
81 25 27513013
134
27543013
130
27573013
134
27603013
0
27633013
159
27663013
123 16 27693013
158
27723013
0
27753013
160
27783013
152
27813013
0
27843013
0
27873013
0
27903013
101
27933013
0
27963013
0
27993013
0
28023013
0
28053013
0
28083013
0
28113013
0
28143013
0
28173013
152
28203013
0
28233013
0
28263013
0
28293013
0
28323013
0
28353013
0
28383013
0
28413013
0
28443013
0
28473013
152
28503013
0
28533013
0
28563013
0
28593013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
14
14
14
16
13
14
13
15
15
14
14
16
14
15
14
16
16
14
14
17
12
14
13
15
13
14
13
15
15
14
15
15
16
13
14
14
15
14
14
16
14
15
14
16
16
15
q
102
109
118
114
143
99
118
102
127
123
122
118
146
127
146
126
159
151
128
120
168
81
102
89
110
103
111
95
123
123
128
144
136
152
100
111
112
123
112
112
136
124
136
120
152
148
128
b f
alg.
0
27223013
0
27253013
0
27283013
0
27313013
0
27343013
0
27373013
118
27403013
0
27433013
0
27463013
0
27493013
122
27523013
86 32 27553013
146
27583013
113 14 27613013
146
27643013
0
27673013
159
27703013
144
7 27733013
0
27763013
0
27793013
168
27823013
0
27853013
0
27883013
0
27913013
0
27943013
0
27973013
0
28003013
0
28033013
122
1 28063013
0
28093013
0
28123013
0
28153013
136
28183013
152
28213013
0
28243013
0
28273013
0
28303013
123
28333013
0
28363013
0
28393013
133
3 28423013
0
28453013
0
28483013
0
28513013
151
1 28543013
148
28573013
0
28603013
189
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
15
14
15
12
14
14
14
14
16
14
15
13
15
15
15
15
17
15
15
11
13
12
14
12
14
14
14
14
16
14
16
15
17
13
15
14
16
14
15
13
15
15
15
15
17
16
q
114
121
115
130
90
115
111
118
114
139
118
134
114
147
139
146
138
171
144
136
69
90
77
98
87
115
115
107
107
135
128
160
136
168
99
124
111
136
112
124
108
140
136
136
132
164
140
b
0
0
0
0
0
0
0
0
0
0
118
134
0
147
132
146
0
171
144
0
0
0
0
0
0
0
0
0
0
135
0
0
132
168
0
119
0
136
0
0
0
139
136
0
0
164
0
f
7
4
5
1
190
alg.
28613013
28643013
28673013
28703013
28733013
28763013
28793013
28823013
28853013
28883013
28913013
28943013
28973013
29003013
29033013
29063013
29093013
29123013
29153013
29183013
29213013
29243013
29273013
29303013
29333013
29363013
29393013
29423013
29453013
29483013
29513013
29543013
29573013
29603013
29633013
29663013
29693013
29723013
29753013
29783013
29813013
29843013
29873013
29903013
29933013
29963013
29993013
ROGER D. MADDUX
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
14
16
16
15
16
16
17
13
13
15
14
15
13
15
16
14
15
15
16
13
15
14
14
16
15
16
13
15
15
15
15
17
15
16
15
17
17
15
14
16
16
17
14
16
17
18
17
q
124
156
152
156
168
168
180
106
102
130
111
127
111
143
147
131
147
140
156
96
120
124
120
152
136
148
111
143
140
139
136
168
152
172
148
184
180
147
139
175
168
191
132
164
180
196
204
b
0
153
149
156
168
168
180
0
0
130
0
0
102
143
147
0
147
0
0
0
0
115
0
148
136
148
0
143
136
0
130
168
149
172
148
184
180
147
0
175
161
191
132
164
180
196
204
f
3
3
9
9
4
4
6
3
7
alg.
28623013
28653013
28683013
28713013
28743013
28773013
28803013
28833013
28863013
28893013
28923013
28953013
28983013
29013013
29043013
29073013
29103013
29133013
29163013
29193013
29223013
29253013
29283013
29313013
29343013
29373013
29403013
29433013
29463013
29493013
29523013
29553013
29583013
29613013
29643013
29673013
29703013
29733013
29763013
29793013
29823013
29853013
29883013
29913013
29943013
29973013
30003013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
15
17
15
17
16
18
13
14
13
15
15
14
15
17
15
16
16
17
14
16
14
15
14
16
16
14
14
16
15
16
14
16
16
16
16
18
16
15
15
17
17
15
16
16
15
16
q
140
136
168
152
188
164
200
102
118
99
127
123
131
135
167
147
163
156
172
108
132
124
136
120
152
148
127
124
156
139
152
136
172
168
168
164
200
163
159
152
188
184
148
164
164
164
180
b f
alg.
0
28633013
0
28663013
165
3 28693013
0
28723013
188
28753013
0
28783013
200
28813013
0
28843013
118
28873013
0
28903013
0
28933013
0
28963013
131
28993013
132
3 29023013
167
29053013
0
29083013
163
29113013
0
29143013
0
29173013
0
29203013
132
29233013
0
29263013
127
9 29293013
117
3 29323013
152
29353013
148
29383013
0
29413013
114 10 29443013
156
29473013
139
29503013
146
6 29533013
133
3 29563013
172
29593013
165
3 29623013
168
29653013
164
29683013
200
29713013
163
29743013
159
29773013
145
7 29803013
188
29833013
177
7 29863013
148
29893013
164
29923013
164
29953013
164
29983013
180
30013013
a
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
c
15
16
14
16
15
17
12
14
14
14
14
16
14
16
13
14
14
15
12
14
13
15
15
15
15
17
14
15
14
16
16
15
15
17
16
17
14
17
15
16
16
18
15
16
17
16
17
q
140
152
136
172
148
184
90
118
114
115
111
139
123
155
115
131
124
140
84
108
108
140
136
136
132
164
127
140
123
155
152
156
152
188
164
184
131
179
155
172
171
204
148
164
180
184
200
b f
134 6
0
0
172
0
184
0
0
114
0
0
0
117
6
155
0
131
0
0
44 40
0
0
137
3
124 12
133
3
132
164
0
134
6
0
155
152
156
149
3
188
164
184
131
179
0
172
0
204
148
164
180
184
200
FINITE INTEGRAL RELATION ALGEBRAS
alg.
30023013
30053013
30083013
30113013
a
5
5
5
5
c
18
18
19
18
q
220
220
236
236
b
220
220
236
236
f
alg.
30033013
30063013
30093013
30123013
a
5
5
5
5
c
16
17
16
19
q
b
180 180
196 196
196 196
256 256
191
f
alg.
30043013
30073013
30103013
30133013
a
5
5
5
5
References
1. Hajnal Andréka and Roger D. Maddux, Representations for small relation algebras, Notre
Dame J. Formal Logic 35 (1994), no. 4, 550–562.
2. Fred Backer, Representable relation algebras, Report for a seminar on relation algebras conducted by A. Tarski, mimeographed, University of California, Berkeley, Spring, 1970.
3. Stephen D. Comer, Multivalued loops and their connection with algebraic logic, 1979, monograph, 173 pp.
4.
, Color schemes forbidding monochrome triangles, Proceedings of the Fourteenth
Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton,
Fla., 1983), vol. 39, 1983, pp. 231–236.
, Constructions of color schemes, Acta Univ. Carolin. Math. Phys. 24 (1983), no. 2,
5.
39–48.
6.
, Extension of polygroups by polygroups and their representations using color schemes,
Universal Algebra and Lattice Theory (Puebla, 1982), Springer, Berlin, 1983, pp. 91–103.
7.
, A new foundation for the theory of relations, Notre Dame J. Formal Logic 24 (1983),
no. 2, 181–187.
8.
, A remark on chromatic polygroups, Congr. Numer. 38 (1983), 85–95.
9.
, Combinatorial aspects of relations, Algebra Universalis 18 (1984), no. 1, 77–94.
10.
, Polygroups derived from cogroups, J. Algebra 89 (1984), no. 2, 397–405.
11.
, Combinatorial types, Algebra, Combinatorics and Logic in Computer Science, Vol. I,
II (GyHor, 1983), North-Holland, Amsterdam, 1986, pp. 267–284.
12.
, Weakly regular trees and their color algebras, Riv. Mat. Pura Appl. (1988), no. 3,
29–37 (1989).
13.
, Multi-Valued Algebras and their Graphical Representation, July 1986, monograph,
103 pp.
14. Robin Hirsch and Ian Hodkinson, Representability is not decidable for finite relation algebras,
Trans. Amer. Math. Soc. 353 (2001), no. 4, 1403–1425 (electronic).
15. Bjarni Jónsson and Alfred Tarski, Boolean algebras with operators. II, Amer. J. Math. 74
(1952), 127–162.
16. Roger C. Lyndon, The representation of relational algebras, Ann. of Math. (2) 51 (1950),
707–729.
17.
, The representation of relation algebras. II, Ann. of Math. (2) 63 (1956), 294–307.
18. Roger D. Maddux, Finite integral relation algebras, Universal Algebra and Lattice Theory
(Charleston, S.C., 1984), Springer, Berlin, 1985, pp. 175–197.
19. Ralph N. McKenzie, The representation of relation algebras, Ph.D. thesis, University of Colorado, Boulder, 1966, pp. vi+128.
20.
, Representations of integral relation algebras, Michigan Math. J. 17 (1970), 279–287.
21. Ulf Wostner, Finite relation algebras, Notices of the American Mathematical Society 23
(1976), A–482.
Department of Mathematics, 396 Carver Hall, Iowa State University, Ames, Iowa
50011, U.S.A.
E-mail address: [email protected]
c
17
18
17
20
q
b
200 200
216 216
216 216
276 276
f