! " # Æ $ % " Æ ! ! " # $%&' ( ) # ! " ! ! ! " " * $% + , %,' - ( !) . " (-) - $%/' $0' 1 * " ( # !) 2 $3' - " " - !# " # $%%' - ! ! !# * " " ! " ! # " # ! ! " " !# # " ! * " # ! - ! ! # # !# 4 # " - * # 5 - # " * " 6 * " " 4 " 7 8 9 " ! - " . # # !# " . # ! :; $<' # !# " = # !# # 5 " ! !# " ! > ! $:' ! ! $%:' ! * ! ( # 7 8) " " " ! ! ! . ? " 4 ! - * 3 > + . " (-) . ? (6 >) " "#* 6 > @ 6 > - ! " - 6=>> $%/' @A-1 $%+' " A " " ? . 4 . @ B B # > ! ( !) ( ! ()( )) 4 () C1 # - # " % 4 ! ( ) ( ) 9 & & ' & () *+ *+ ' ¼ ¼ , -- *+ ( ) ( ) 4 D - E ! ! " 7 D8 ( D) 4 D D " D 4 " ! " D * # - 7"8 D ( ) " ! #" * # D - 4 # - # " # Æ # !# ! ! " ! $%3 %0 /' # " " ! 4 " # " ! - ! $F' # . " . 4 & # & * G % . 4 7 8 7! 8 . 4 4 " (#) B ( ) " " " 4 # ( ) ! ( ) " & $/' ! ¼ ¼ ¼ ¼ ? ! 7 8 H H ) B ( ) H B (H H H H ( ?) ? H H 5 Æ H $%&' 78 H ( ) - " H H 4 H 4 ! " H ! 5 Æ H ! H H H ! ! " " H 78 H H - H H H (H ) " H H - H 9 ¼ ( ) ¾ ( H()) - " ! 5 " - # $3' " ( !# ) 4 ! ? " 9 () B & () " H ! H H¼ B (H ( ) H ( ) H ( )) - H ! H H H " H ! H ¼ ¼ ¼ ! $%%' ! ! # ! 5 H B ( ) " ! # " ! Æ ! > ! " - " ! ! ! # - !# ! " ! $%%' ? " ## Æ ! = - ! ! D ! H ! - # - !# - H() H ! 4 ! 4 ( ) # " 4 7 8 - H 4 - H() # D ! ! # H D H # ! # H > 33 # !# H H ! ! H 78 " ! - # 5 - D 3E: # 4 # D 3E: ! 5 # - H $ # Æ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hybrid runtime (seconds) 1000 100 10 1 0.1 0.1 1 10 100 proof based time (seconds) 1000 10000 < $ 3 + # ( # ) 4 !# 4 " :; > / 3 # ! 4 * " # . :F& # ! %F; # = " > /, # # # 10000 hybrid time (seconds) 1000 100 10 1 0.1 0.1 1 10 100 CEX time (seconds) 1000 10000 < $ ! 4 !# # " !# " # * " A ! # ! - ! 5 7 8 - ! " " " ! " = # !# # > 7 8 * * " 2 # , * = * 3;>65 2;;4 3 ? < , @ A B - AA - ? $ ' 25 ? 2;;5 4 @ ? B $ = C * & ) 3553 6 @ A D E ? F - $ = 276>28; 3555 7 @ A * E ? B D *+ - ! 3553 8 A E E B A$ < # A F = A 3554 9 E E% - E % 3555 : * E A E G F * 3554 ; D B A F = A ! "! ! # 2;.40'3;2>426 3552 25 < B $ $ # %!!! ( 2;;6 22 B - AA ) * * 3554 23 A C A # A F G - G A "' @ Æ *+ ! # 745>747 3552 24 * D - %&% 2;:7 26 ? A B * E<* > 2;;8 27 AF = C * # '( 433>442 2;:8 28 C , - $ ? E $ # H 3554 29 C $ ? - ? $ B F G $ + A < # ! # 47>65 3552
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