/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern log2(a,g) w.r.t. the given Prolog program could not be shown: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 12 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [EQUIVALENT, 0 ms] (11) QDP (12) MRRProof [EQUIVALENT, 47 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) TRUE (16) PiDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) PiDP (19) PiDPToQDPProof [SOUND, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) NonTerminationLoopProof [COMPLETE, 0 ms] (26) NO (27) PrologToPiTRSProof [SOUND, 0 ms] (28) PiTRS (29) DependencyPairsProof [EQUIVALENT, 3 ms] (30) PiDP (31) DependencyGraphProof [EQUIVALENT, 0 ms] (32) AND (33) PiDP (34) UsableRulesProof [EQUIVALENT, 0 ms] (35) PiDP (36) PiDPToQDPProof [SOUND, 0 ms] (37) QDP (38) MRRProof [EQUIVALENT, 66 ms] (39) QDP (40) DependencyGraphProof [EQUIVALENT, 0 ms] (41) TRUE (42) PiDP (43) UsableRulesProof [EQUIVALENT, 0 ms] (44) PiDP (45) PiDPToQDPProof [SOUND, 0 ms] (46) QDP (47) TransformationProof [EQUIVALENT, 0 ms] (48) QDP (49) TransformationProof [EQUIVALENT, 0 ms] (50) QDP (51) NonTerminationLoopProof [COMPLETE, 0 ms] (52) NO (53) PrologToTRSTransformerProof [SOUND, 1758 ms] (54) QTRS (55) DependencyPairsProof [EQUIVALENT, 80 ms] (56) QDP (57) DependencyGraphProof [EQUIVALENT, 0 ms] (58) AND (59) QDP (60) UsableRulesProof [EQUIVALENT, 0 ms] (61) QDP (62) MRRProof [EQUIVALENT, 0 ms] (63) QDP (64) PisEmptyProof [EQUIVALENT, 0 ms] (65) YES (66) QDP (67) UsableRulesProof [EQUIVALENT, 0 ms] (68) QDP (69) QDPSizeChangeProof [EQUIVALENT, 0 ms] (70) YES (71) QDP (72) UsableRulesProof [EQUIVALENT, 0 ms] (73) QDP (74) QDPSizeChangeProof [EQUIVALENT, 0 ms] (75) YES (76) QDP (77) UsableRulesProof [EQUIVALENT, 0 ms] (78) QDP (79) QDPSizeChangeProof [EQUIVALENT, 0 ms] (80) YES (81) QDP (82) UsableRulesProof [EQUIVALENT, 0 ms] (83) QDP (84) QDPSizeChangeProof [EQUIVALENT, 0 ms] (85) YES (86) QDP (87) UsableRulesProof [EQUIVALENT, 0 ms] (88) QDP (89) QDPSizeChangeProof [EQUIVALENT, 0 ms] (90) YES (91) QDP (92) UsableRulesProof [EQUIVALENT, 0 ms] (93) QDP (94) QDPSizeChangeProof [EQUIVALENT, 0 ms] (95) YES (96) QDP (97) UsableRulesProof [EQUIVALENT, 0 ms] (98) QDP (99) TransformationProof [EQUIVALENT, 0 ms] (100) QDP (101) TransformationProof [EQUIVALENT, 0 ms] (102) QDP (103) NonTerminationLoopProof [COMPLETE, 0 ms] (104) NO (105) PrologToDTProblemTransformerProof [SOUND, 1797 ms] (106) TRIPLES (107) TriplesToPiDPProof [SOUND, 733 ms] (108) PiDP (109) DependencyGraphProof [EQUIVALENT, 0 ms] (110) AND (111) PiDP (112) PiDPToQDPProof [EQUIVALENT, 0 ms] (113) QDP (114) MRRProof [EQUIVALENT, 0 ms] (115) QDP (116) PisEmptyProof [EQUIVALENT, 0 ms] (117) YES (118) PiDP (119) PiDPToQDPProof [EQUIVALENT, 0 ms] (120) QDP (121) QDPSizeChangeProof [EQUIVALENT, 0 ms] (122) YES (123) PiDP (124) PiDPToQDPProof [EQUIVALENT, 0 ms] (125) QDP (126) QDPSizeChangeProof [EQUIVALENT, 0 ms] (127) YES (128) PiDP (129) PiDPToQDPProof [EQUIVALENT, 0 ms] (130) QDP (131) QDPSizeChangeProof [EQUIVALENT, 0 ms] (132) YES (133) PiDP (134) PiDPToQDPProof [EQUIVALENT, 0 ms] (135) QDP (136) QDPSizeChangeProof [EQUIVALENT, 0 ms] (137) YES (138) PiDP (139) PiDPToQDPProof [EQUIVALENT, 0 ms] (140) QDP (141) QDPSizeChangeProof [EQUIVALENT, 0 ms] (142) YES (143) PiDP (144) PiDPToQDPProof [EQUIVALENT, 0 ms] (145) QDP (146) QDPSizeChangeProof [EQUIVALENT, 0 ms] (147) YES (148) PiDP (149) PiDPToQDPProof [SOUND, 0 ms] (150) QDP (151) TransformationProof [EQUIVALENT, 0 ms] (152) QDP (153) TransformationProof [EQUIVALENT, 0 ms] (154) QDP (155) NonTerminationLoopProof [COMPLETE, 0 ms] (156) NO ---------------------------------------- (0) Obligation: Clauses: log2(X, Y) :- log2(X, 0, s(0), Y). log2(s(s(X)), Half, Acc, Y) :- log2(X, s(Half), Acc, Y). log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y)). log2(X, Half, Y, Y) :- ','(small(X), small(Half)). small(0). small(s(0)). Query: log2(a,g) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: log2_in_2: (f,b) log2_in_4: (f,b,b,b) (b,b,b,b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_aggg(X, 0, s(0), Y)) LOG2_IN_AG(X, Y) -> LOG2_IN_AGGG(X, 0, s(0), Y) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> U2_AGGG(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> U3_AGGG(X, Half, Acc, Y, small_in_a(X)) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_A(X) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> U4_AGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> U2_GGGG(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_G(X) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> U4_GGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(X, Half, Y, Y) -> U5_GGGG(X, Half, Y, small_in_g(X)) LOG2_IN_GGGG(X, Half, Y, Y) -> SMALL_IN_G(X) U5_GGGG(X, Half, Y, small_out_g(X)) -> U6_GGGG(X, Half, Y, small_in_g(Half)) U5_GGGG(X, Half, Y, small_out_g(X)) -> SMALL_IN_G(Half) LOG2_IN_AGGG(X, Half, Y, Y) -> U5_AGGG(X, Half, Y, small_in_a(X)) LOG2_IN_AGGG(X, Half, Y, Y) -> SMALL_IN_A(X) U5_AGGG(X, Half, Y, small_out_a(X)) -> U6_AGGG(X, Half, Y, small_in_g(Half)) U5_AGGG(X, Half, Y, small_out_a(X)) -> SMALL_IN_G(Half) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) U1_AG(x1, x2, x3) = U1_AG(x2, x3) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) U2_AGGG(x1, x2, x3, x4, x5) = U2_AGGG(x2, x3, x4, x5) U3_AGGG(x1, x2, x3, x4, x5) = U3_AGGG(x2, x3, x4, x5) SMALL_IN_A(x1) = SMALL_IN_A U4_AGGG(x1, x2, x3, x4, x5) = U4_AGGG(x1, x2, x3, x4, x5) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U2_GGGG(x1, x2, x3, x4, x5) = U2_GGGG(x1, x2, x3, x4, x5) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x1, x2, x3, x4, x5) SMALL_IN_G(x1) = SMALL_IN_G(x1) U4_GGGG(x1, x2, x3, x4, x5) = U4_GGGG(x1, x2, x3, x4, x5) U5_GGGG(x1, x2, x3, x4) = U5_GGGG(x1, x2, x3, x4) U6_GGGG(x1, x2, x3, x4) = U6_GGGG(x1, x2, x3, x4) U5_AGGG(x1, x2, x3, x4) = U5_AGGG(x2, x3, x4) U6_AGGG(x1, x2, x3, x4) = U6_AGGG(x1, x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (4) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_aggg(X, 0, s(0), Y)) LOG2_IN_AG(X, Y) -> LOG2_IN_AGGG(X, 0, s(0), Y) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> U2_AGGG(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> U3_AGGG(X, Half, Acc, Y, small_in_a(X)) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_A(X) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> U4_AGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> U2_GGGG(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_G(X) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> U4_GGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(X, Half, Y, Y) -> U5_GGGG(X, Half, Y, small_in_g(X)) LOG2_IN_GGGG(X, Half, Y, Y) -> SMALL_IN_G(X) U5_GGGG(X, Half, Y, small_out_g(X)) -> U6_GGGG(X, Half, Y, small_in_g(Half)) U5_GGGG(X, Half, Y, small_out_g(X)) -> SMALL_IN_G(Half) LOG2_IN_AGGG(X, Half, Y, Y) -> U5_AGGG(X, Half, Y, small_in_a(X)) LOG2_IN_AGGG(X, Half, Y, Y) -> SMALL_IN_A(X) U5_AGGG(X, Half, Y, small_out_a(X)) -> U6_AGGG(X, Half, Y, small_in_g(Half)) U5_AGGG(X, Half, Y, small_out_a(X)) -> SMALL_IN_G(Half) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) U1_AG(x1, x2, x3) = U1_AG(x2, x3) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) U2_AGGG(x1, x2, x3, x4, x5) = U2_AGGG(x2, x3, x4, x5) U3_AGGG(x1, x2, x3, x4, x5) = U3_AGGG(x2, x3, x4, x5) SMALL_IN_A(x1) = SMALL_IN_A U4_AGGG(x1, x2, x3, x4, x5) = U4_AGGG(x1, x2, x3, x4, x5) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U2_GGGG(x1, x2, x3, x4, x5) = U2_GGGG(x1, x2, x3, x4, x5) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x1, x2, x3, x4, x5) SMALL_IN_G(x1) = SMALL_IN_G(x1) U4_GGGG(x1, x2, x3, x4, x5) = U4_GGGG(x1, x2, x3, x4, x5) U5_GGGG(x1, x2, x3, x4) = U5_GGGG(x1, x2, x3, x4) U6_GGGG(x1, x2, x3, x4) = U6_GGGG(x1, x2, x3, x4) U5_AGGG(x1, x2, x3, x4) = U5_AGGG(x2, x3, x4) U6_AGGG(x1, x2, x3, x4) = U6_AGGG(x1, x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 18 less nodes. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x1, x2, x3, x4, x5) We have to consider all (P,R,Pi)-chains ---------------------------------------- (8) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (9) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (10) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) The set Q consists of the following terms: small_in_g(x0) We have to consider all (P,Q,R)-chains. ---------------------------------------- (12) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) Strictly oriented rules of the TRS R: small_in_g(0) -> small_out_g(0) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(LOG2_IN_GGGG(x_1, x_2, x_3, x_4)) = 2*x_1 + 2*x_2 + x_3 + x_4 POL(U3_GGGG(x_1, x_2, x_3, x_4, x_5)) = 2 + x_1 + 2*x_2 + x_3 + x_4 + x_5 POL(s(x_1)) = 1 + x_1 POL(small_in_g(x_1)) = 2 + x_1 POL(small_out_g(x_1)) = 1 + 2*x_1 ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) The TRS R consists of the following rules: small_in_g(s(0)) -> small_out_g(s(0)) The set Q consists of the following terms: small_in_g(x0) We have to consider all (P,Q,R)-chains. ---------------------------------------- (14) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes. ---------------------------------------- (15) TRUE ---------------------------------------- (16) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x2, x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x2, x3, x4, x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x2, x3, x4, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x1, x2, x3, x4, x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x1, x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g(x1) U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x1, x2, x3, x4, x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x1, x2, x3, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x1, x2, x3, x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg(x1, x2, x3, x4) log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1, x2, x3, x4) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x3, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x2, x3, x4) log2_out_ag(x1, x2) = log2_out_ag(x1, x2) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (17) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (18) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) R is empty. The argument filtering Pi contains the following mapping: s(x1) = s(x1) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (19) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(Half, Acc, Y) -> LOG2_IN_AGGG(s(Half), Acc, Y) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (21) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2_IN_AGGG(Half, Acc, Y) -> LOG2_IN_AGGG(s(Half), Acc, Y) we obtained the following new rules [LPAR04]: (LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2),LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2)) ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (23) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2) we obtained the following new rules [LPAR04]: (LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2),LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2)) ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (25) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = LOG2_IN_AGGG(s(s(z0)), z1, z2) evaluates to t =LOG2_IN_AGGG(s(s(s(z0))), z1, z2) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [z0 / s(z0)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from LOG2_IN_AGGG(s(s(z0)), z1, z2) to LOG2_IN_AGGG(s(s(s(z0))), z1, z2). ---------------------------------------- (26) NO ---------------------------------------- (27) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: log2_in_2: (f,b) log2_in_4: (f,b,b,b) (b,b,b,b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (28) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) ---------------------------------------- (29) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_aggg(X, 0, s(0), Y)) LOG2_IN_AG(X, Y) -> LOG2_IN_AGGG(X, 0, s(0), Y) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> U2_AGGG(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> U3_AGGG(X, Half, Acc, Y, small_in_a(X)) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_A(X) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> U4_AGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> U2_GGGG(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_G(X) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> U4_GGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(X, Half, Y, Y) -> U5_GGGG(X, Half, Y, small_in_g(X)) LOG2_IN_GGGG(X, Half, Y, Y) -> SMALL_IN_G(X) U5_GGGG(X, Half, Y, small_out_g(X)) -> U6_GGGG(X, Half, Y, small_in_g(Half)) U5_GGGG(X, Half, Y, small_out_g(X)) -> SMALL_IN_G(Half) LOG2_IN_AGGG(X, Half, Y, Y) -> U5_AGGG(X, Half, Y, small_in_a(X)) LOG2_IN_AGGG(X, Half, Y, Y) -> SMALL_IN_A(X) U5_AGGG(X, Half, Y, small_out_a(X)) -> U6_AGGG(X, Half, Y, small_in_g(Half)) U5_AGGG(X, Half, Y, small_out_a(X)) -> SMALL_IN_G(Half) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) U1_AG(x1, x2, x3) = U1_AG(x3) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) U2_AGGG(x1, x2, x3, x4, x5) = U2_AGGG(x5) U3_AGGG(x1, x2, x3, x4, x5) = U3_AGGG(x2, x3, x4, x5) SMALL_IN_A(x1) = SMALL_IN_A U4_AGGG(x1, x2, x3, x4, x5) = U4_AGGG(x1, x5) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U2_GGGG(x1, x2, x3, x4, x5) = U2_GGGG(x5) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x2, x3, x4, x5) SMALL_IN_G(x1) = SMALL_IN_G(x1) U4_GGGG(x1, x2, x3, x4, x5) = U4_GGGG(x5) U5_GGGG(x1, x2, x3, x4) = U5_GGGG(x2, x4) U6_GGGG(x1, x2, x3, x4) = U6_GGGG(x4) U5_AGGG(x1, x2, x3, x4) = U5_AGGG(x2, x4) U6_AGGG(x1, x2, x3, x4) = U6_AGGG(x1, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (30) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_aggg(X, 0, s(0), Y)) LOG2_IN_AG(X, Y) -> LOG2_IN_AGGG(X, 0, s(0), Y) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> U2_AGGG(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> U3_AGGG(X, Half, Acc, Y, small_in_a(X)) LOG2_IN_AGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_A(X) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> U4_AGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_AGGG(X, Half, Acc, Y, small_out_a(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> U2_GGGG(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> SMALL_IN_G(X) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> U4_GGGG(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(X, Half, Y, Y) -> U5_GGGG(X, Half, Y, small_in_g(X)) LOG2_IN_GGGG(X, Half, Y, Y) -> SMALL_IN_G(X) U5_GGGG(X, Half, Y, small_out_g(X)) -> U6_GGGG(X, Half, Y, small_in_g(Half)) U5_GGGG(X, Half, Y, small_out_g(X)) -> SMALL_IN_G(Half) LOG2_IN_AGGG(X, Half, Y, Y) -> U5_AGGG(X, Half, Y, small_in_a(X)) LOG2_IN_AGGG(X, Half, Y, Y) -> SMALL_IN_A(X) U5_AGGG(X, Half, Y, small_out_a(X)) -> U6_AGGG(X, Half, Y, small_in_g(Half)) U5_AGGG(X, Half, Y, small_out_a(X)) -> SMALL_IN_G(Half) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) U1_AG(x1, x2, x3) = U1_AG(x3) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) U2_AGGG(x1, x2, x3, x4, x5) = U2_AGGG(x5) U3_AGGG(x1, x2, x3, x4, x5) = U3_AGGG(x2, x3, x4, x5) SMALL_IN_A(x1) = SMALL_IN_A U4_AGGG(x1, x2, x3, x4, x5) = U4_AGGG(x1, x5) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U2_GGGG(x1, x2, x3, x4, x5) = U2_GGGG(x5) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x2, x3, x4, x5) SMALL_IN_G(x1) = SMALL_IN_G(x1) U4_GGGG(x1, x2, x3, x4, x5) = U4_GGGG(x5) U5_GGGG(x1, x2, x3, x4) = U5_GGGG(x2, x4) U6_GGGG(x1, x2, x3, x4) = U6_GGGG(x4) U5_AGGG(x1, x2, x3, x4) = U5_AGGG(x2, x4) U6_AGGG(x1, x2, x3, x4) = U6_AGGG(x1, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (31) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 18 less nodes. ---------------------------------------- (32) Complex Obligation (AND) ---------------------------------------- (33) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x2, x3, x4, x5) We have to consider all (P,R,Pi)-chains ---------------------------------------- (34) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (35) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(X, Half, Acc, Y, small_in_g(X)) U3_GGGG(X, Half, Acc, Y, small_out_g(X)) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) The argument filtering Pi contains the following mapping: s(x1) = s(x1) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g LOG2_IN_GGGG(x1, x2, x3, x4) = LOG2_IN_GGGG(x1, x2, x3, x4) U3_GGGG(x1, x2, x3, x4, x5) = U3_GGGG(x2, x3, x4, x5) We have to consider all (P,R,Pi)-chains ---------------------------------------- (36) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(Half, Acc, Y, small_in_g(X)) U3_GGGG(Half, Acc, Y, small_out_g) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: small_in_g(0) -> small_out_g small_in_g(s(0)) -> small_out_g The set Q consists of the following terms: small_in_g(x0) We have to consider all (P,Q,R)-chains. ---------------------------------------- (38) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: U3_GGGG(Half, Acc, Y, small_out_g) -> LOG2_IN_GGGG(Half, s(0), s(Acc), Y) LOG2_IN_GGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_GGGG(X, s(Half), Acc, Y) Strictly oriented rules of the TRS R: small_in_g(s(0)) -> small_out_g Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(LOG2_IN_GGGG(x_1, x_2, x_3, x_4)) = 2*x_1 + 2*x_2 + x_3 + x_4 POL(U3_GGGG(x_1, x_2, x_3, x_4)) = 2*x_1 + x_2 + x_3 + 2*x_4 POL(s(x_1)) = 1 + x_1 POL(small_in_g(x_1)) = 2 + x_1 POL(small_out_g) = 2 ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_GGGG(X, s(s(Half)), Acc, Y) -> U3_GGGG(Half, Acc, Y, small_in_g(X)) The TRS R consists of the following rules: small_in_g(0) -> small_out_g The set Q consists of the following terms: small_in_g(x0) We have to consider all (P,Q,R)-chains. ---------------------------------------- (40) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (41) TRUE ---------------------------------------- (42) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) The TRS R consists of the following rules: log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_aggg(X, 0, s(0), Y)) log2_in_aggg(s(s(X)), Half, Acc, Y) -> U2_aggg(X, Half, Acc, Y, log2_in_aggg(X, s(Half), Acc, Y)) log2_in_aggg(X, s(s(Half)), Acc, Y) -> U3_aggg(X, Half, Acc, Y, small_in_a(X)) small_in_a(0) -> small_out_a(0) small_in_a(s(0)) -> small_out_a(s(0)) U3_aggg(X, Half, Acc, Y, small_out_a(X)) -> U4_aggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(s(s(X)), Half, Acc, Y) -> U2_gggg(X, Half, Acc, Y, log2_in_gggg(X, s(Half), Acc, Y)) log2_in_gggg(X, s(s(Half)), Acc, Y) -> U3_gggg(X, Half, Acc, Y, small_in_g(X)) small_in_g(0) -> small_out_g(0) small_in_g(s(0)) -> small_out_g(s(0)) U3_gggg(X, Half, Acc, Y, small_out_g(X)) -> U4_gggg(X, Half, Acc, Y, log2_in_gggg(Half, s(0), s(Acc), Y)) log2_in_gggg(X, Half, Y, Y) -> U5_gggg(X, Half, Y, small_in_g(X)) U5_gggg(X, Half, Y, small_out_g(X)) -> U6_gggg(X, Half, Y, small_in_g(Half)) U6_gggg(X, Half, Y, small_out_g(Half)) -> log2_out_gggg(X, Half, Y, Y) U4_gggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_gggg(X, s(s(Half)), Acc, Y) U2_gggg(X, Half, Acc, Y, log2_out_gggg(X, s(Half), Acc, Y)) -> log2_out_gggg(s(s(X)), Half, Acc, Y) U4_aggg(X, Half, Acc, Y, log2_out_gggg(Half, s(0), s(Acc), Y)) -> log2_out_aggg(X, s(s(Half)), Acc, Y) log2_in_aggg(X, Half, Y, Y) -> U5_aggg(X, Half, Y, small_in_a(X)) U5_aggg(X, Half, Y, small_out_a(X)) -> U6_aggg(X, Half, Y, small_in_g(Half)) U6_aggg(X, Half, Y, small_out_g(Half)) -> log2_out_aggg(X, Half, Y, Y) U2_aggg(X, Half, Acc, Y, log2_out_aggg(X, s(Half), Acc, Y)) -> log2_out_aggg(s(s(X)), Half, Acc, Y) U1_ag(X, Y, log2_out_aggg(X, 0, s(0), Y)) -> log2_out_ag(X, Y) The argument filtering Pi contains the following mapping: log2_in_ag(x1, x2) = log2_in_ag(x2) U1_ag(x1, x2, x3) = U1_ag(x3) log2_in_aggg(x1, x2, x3, x4) = log2_in_aggg(x2, x3, x4) U2_aggg(x1, x2, x3, x4, x5) = U2_aggg(x5) s(x1) = s(x1) U3_aggg(x1, x2, x3, x4, x5) = U3_aggg(x2, x3, x4, x5) small_in_a(x1) = small_in_a small_out_a(x1) = small_out_a(x1) U4_aggg(x1, x2, x3, x4, x5) = U4_aggg(x1, x5) log2_in_gggg(x1, x2, x3, x4) = log2_in_gggg(x1, x2, x3, x4) U2_gggg(x1, x2, x3, x4, x5) = U2_gggg(x5) U3_gggg(x1, x2, x3, x4, x5) = U3_gggg(x2, x3, x4, x5) small_in_g(x1) = small_in_g(x1) 0 = 0 small_out_g(x1) = small_out_g U4_gggg(x1, x2, x3, x4, x5) = U4_gggg(x5) U5_gggg(x1, x2, x3, x4) = U5_gggg(x2, x4) U6_gggg(x1, x2, x3, x4) = U6_gggg(x4) log2_out_gggg(x1, x2, x3, x4) = log2_out_gggg log2_out_aggg(x1, x2, x3, x4) = log2_out_aggg(x1) U5_aggg(x1, x2, x3, x4) = U5_aggg(x2, x4) U6_aggg(x1, x2, x3, x4) = U6_aggg(x1, x4) log2_out_ag(x1, x2) = log2_out_ag(x1) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (43) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (44) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(X)), Half, Acc, Y) -> LOG2_IN_AGGG(X, s(Half), Acc, Y) R is empty. The argument filtering Pi contains the following mapping: s(x1) = s(x1) LOG2_IN_AGGG(x1, x2, x3, x4) = LOG2_IN_AGGG(x2, x3, x4) We have to consider all (P,R,Pi)-chains ---------------------------------------- (45) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(Half, Acc, Y) -> LOG2_IN_AGGG(s(Half), Acc, Y) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (47) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2_IN_AGGG(Half, Acc, Y) -> LOG2_IN_AGGG(s(Half), Acc, Y) we obtained the following new rules [LPAR04]: (LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2),LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2)) ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (49) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2_IN_AGGG(s(z0), z1, z2) -> LOG2_IN_AGGG(s(s(z0)), z1, z2) we obtained the following new rules [LPAR04]: (LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2),LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2)) ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2_IN_AGGG(s(s(z0)), z1, z2) -> LOG2_IN_AGGG(s(s(s(z0))), z1, z2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (51) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = LOG2_IN_AGGG(s(s(z0)), z1, z2) evaluates to t =LOG2_IN_AGGG(s(s(s(z0))), z1, z2) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [z0 / s(z0)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from LOG2_IN_AGGG(s(s(z0)), z1, z2) to LOG2_IN_AGGG(s(s(s(z0))), z1, z2). ---------------------------------------- (52) NO ---------------------------------------- (53) PrologToTRSTransformerProof (SOUND) Transformed Prolog program to TRS. { "root": 3, "program": { "directives": [], "clauses": [ [ "(log2 X Y)", "(log2 X (0) (s (0)) Y)" ], [ "(log2 (s (s X)) Half Acc Y)", "(log2 X (s Half) Acc Y)" ], [ "(log2 X (s (s Half)) Acc Y)", "(',' (small X) (log2 Half (s (0)) (s Acc) Y))" ], [ "(log2 X Half Y Y)", "(',' (small X) (small Half))" ], [ "(small (0))", null ], [ "(small (s (0)))", null ] ] }, "graph": { "nodes": { "4970": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1461": { "goal": [ { "clause": 2, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" }, { "clause": 3, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T928", "T929", "T930" ], "free": [], "exprvars": [] } }, "1460": { "goal": [{ "clause": 1, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T928", "T929", "T930" ], "free": [], "exprvars": [] } }, "2791": { "goal": [{ "clause": 3, "scope": 53, "term": "(log2 T718 (s (s (s (s (s (s (0))))))) (s (s (s (s (s (s (0))))))) T719)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T718", "T719" ], "free": [], "exprvars": [] } }, "2790": { "goal": [{ "clause": 2, "scope": 53, "term": "(log2 T718 (s (s (s (s (s (s (0))))))) (s (s (s (s (s (s (0))))))) T719)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T718", "T719" ], "free": [], "exprvars": [] } }, "2306": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (0)))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4969": { "goal": [{ "clause": 5, "scope": 247, "term": "(small (s (s (s (0)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2305": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1457": { "goal": [ { "clause": 1, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" }, { "clause": 2, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" }, { "clause": 3, "scope": 67, "term": "(log2 T928 (s (s (0))) (s T929) T930)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T928", "T929", "T930" ], "free": [], "exprvars": [] } }, "2304": { "goal": [{ "clause": 5, "scope": 118, "term": "(small (s (s (s (s (s (0)))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1456": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2303": { "goal": [ { "clause": 4, "scope": 118, "term": "(small (s (s (s (s (s (0)))))))" }, { "clause": 5, "scope": 118, "term": "(small (s (s (s (s (s (0)))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1455": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 T928 (s (s (0))) (s T929) T930)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T928", "T929", "T930" ], "free": [], "exprvars": [] } }, "2302": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2301": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (0)))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2300": { "goal": [{ "clause": 5, "scope": 117, "term": "(',' (small T1343) (small (s (s (s (s (s (0))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1343"], "free": [], "exprvars": [] } }, "4961": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4962": { "goal": [ { "clause": 4, "scope": 246, "term": "(small (s (s (s (0)))))" }, { "clause": 5, "scope": 246, "term": "(small (s (s (s (0)))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4963": { "goal": [{ "clause": 5, "scope": 246, "term": "(small (s (s 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{ "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3628": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4956": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5803": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3627": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 (s (s (s (0)))) (s (0)) (s (s (s (s (s (s (0))))))) T1557)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1557"], "free": [], "exprvars": [] } }, "4957": { "goal": [ { "clause": 4, "scope": 245, "term": "(',' (small T1814) (small (s (s (s (0))))))" }, { "clause": 5, "scope": 245, "term": "(',' (small T1814) (small (s (s (s (0))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1814"], "free": [], "exprvars": [] } }, "5804": { "goal": [ { "clause": 4, "scope": 291, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }, { "clause": 5, "scope": 291, "term": "(small (s (s (s (s (s (s (s (0)))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 3, "to": 5, "label": "CASE" }, { "from": 5, "to": 179, "label": "ONLY EVAL with clause\nlog2(X9, X10) :- log2(X9, 0, s(0), X10).\nand substitutionT1 -> T12,\nX9 -> T12,\nT2 -> T11,\nX10 -> T11,\nT10 -> T12" }, { "from": 179, "to": 255, "label": "CASE" }, { "from": 255, "to": 256, "label": "PARALLEL" }, { "from": 255, "to": 258, "label": "PARALLEL" }, { "from": 256, "to": 274, "label": "EVAL with clause\nlog2(s(s(X31)), X32, X33, X34) :- log2(X31, s(X32), X33, X34).\nand substitutionX31 -> T25,\nT12 -> s(s(T25)),\nX32 -> 0,\nX33 -> s(0),\nT11 -> T24,\nX34 -> T24,\nT23 -> T25" }, { "from": 256, "to": 277, "label": "EVAL-BACKTRACK" }, { "from": 258, "to": 6220, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 274, "to": 282, "label": "CASE" }, { "from": 282, "to": 284, "label": "PARALLEL" }, { "from": 282, "to": 285, "label": "PARALLEL" }, { "from": 284, "to": 288, "label": "EVAL with clause\nlog2(s(s(X55)), X56, X57, X58) :- log2(X55, s(X56), X57, X58).\nand substitutionX55 -> T38,\nT25 -> s(s(T38)),\nX56 -> s(0),\nX57 -> s(0),\nT24 -> T37,\nX58 -> T37,\nT36 -> T38" }, { "from": 284, "to": 289, "label": "EVAL-BACKTRACK" }, { "from": 285, "to": 6194, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 288, "to": 290, "label": "CASE" }, { "from": 290, "to": 296, "label": "PARALLEL" }, { "from": 290, "to": 297, "label": "PARALLEL" }, { "from": 296, "to": 312, "label": "EVAL with clause\nlog2(s(s(X79)), X80, X81, X82) :- log2(X79, s(X80), X81, X82).\nand substitutionX79 -> T51,\nT38 -> s(s(T51)),\nX80 -> s(s(0)),\nX81 -> s(0),\nT37 -> T50,\nX82 -> T50,\nT49 -> T51" }, { "from": 296, "to": 313, "label": "EVAL-BACKTRACK" }, { "from": 297, "to": 6111, "label": "PARALLEL" }, { "from": 297, "to": 6112, "label": "PARALLEL" }, { "from": 312, "to": 316, "label": "CASE" }, { "from": 316, "to": 319, "label": "PARALLEL" }, { "from": 316, "to": 320, "label": "PARALLEL" }, { "from": 319, "to": 326, "label": "EVAL with clause\nlog2(s(s(X103)), X104, X105, X106) :- log2(X103, s(X104), X105, X106).\nand substitutionX103 -> T64,\nT51 -> s(s(T64)),\nX104 -> s(s(s(0))),\nX105 -> s(0),\nT50 -> T63,\nX106 -> T63,\nT62 -> T64" }, { "from": 319, "to": 327, "label": "EVAL-BACKTRACK" }, { "from": 320, "to": 6035, "label": "PARALLEL" }, { "from": 320, "to": 6036, "label": "PARALLEL" }, { "from": 326, "to": 330, "label": "CASE" }, { "from": 330, "to": 334, "label": "PARALLEL" }, { "from": 330, "to": 335, "label": "PARALLEL" }, { "from": 334, "to": 338, "label": "EVAL with clause\nlog2(s(s(X127)), X128, X129, X130) :- log2(X127, s(X128), X129, X130).\nand substitutionX127 -> T77,\nT64 -> s(s(T77)),\nX128 -> s(s(s(s(0)))),\nX129 -> s(0),\nT63 -> T76,\nX130 -> T76,\nT75 -> T77" }, { "from": 334, "to": 339, "label": "EVAL-BACKTRACK" }, { "from": 335, "to": 5955, "label": "PARALLEL" }, { "from": 335, "to": 5956, "label": "PARALLEL" }, { "from": 338, "to": 348, "label": "CASE" }, { "from": 348, "to": 350, "label": "PARALLEL" }, { "from": 348, "to": 351, "label": "PARALLEL" }, { "from": 350, "to": 353, "label": "EVAL with clause\nlog2(s(s(X151)), X152, X153, X154) :- log2(X151, s(X152), X153, X154).\nand substitutionX151 -> T90,\nT77 -> s(s(T90)),\nX152 -> s(s(s(s(s(0))))),\nX153 -> s(0),\nT76 -> T89,\nX154 -> T89,\nT88 -> T90" }, { "from": 350, "to": 354, "label": "EVAL-BACKTRACK" }, { "from": 351, "to": 5889, "label": "PARALLEL" }, { "from": 351, "to": 5890, "label": "PARALLEL" }, { "from": 353, "to": 357, "label": "CASE" }, { "from": 357, "to": 358, "label": "PARALLEL" }, { "from": 357, "to": 359, "label": "PARALLEL" }, { "from": 358, "to": 384, "label": "EVAL with clause\nlog2(s(s(X175)), X176, X177, X178) :- log2(X175, s(X176), X177, X178).\nand substitutionX175 -> T103,\nT90 -> s(s(T103)),\nX176 -> s(s(s(s(s(s(0)))))),\nX177 -> s(0),\nT89 -> T102,\nX178 -> T102,\nT101 -> T103" }, { "from": 358, "to": 385, "label": "EVAL-BACKTRACK" }, { "from": 359, "to": 5814, "label": "PARALLEL" }, { "from": 359, "to": 5815, "label": "PARALLEL" }, { "from": 384, "to": 403, "label": "CASE" }, { "from": 403, "to": 404, "label": "PARALLEL" }, { "from": 403, "to": 405, "label": "PARALLEL" }, { "from": 404, "to": 428, "label": "EVAL with clause\nlog2(s(s(X199)), X200, X201, X202) :- log2(X199, s(X200), X201, X202).\nand substitutionX199 -> T116,\nT103 -> s(s(T116)),\nX200 -> s(s(s(s(s(s(s(0))))))),\nX201 -> s(0),\nT102 -> T115,\nX202 -> T115,\nT114 -> T116" }, { "from": 404, "to": 429, "label": "EVAL-BACKTRACK" }, { "from": 405, "to": 5735, "label": "PARALLEL" }, { "from": 405, "to": 5736, "label": "PARALLEL" }, { "from": 428, "to": 430, "label": "GENERALIZATION\nT119 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT119 is ground" }, { "from": 430, "to": 431, "label": "CASE" }, { "from": 431, "to": 432, "label": "PARALLEL" }, { "from": 431, "to": 433, "label": "PARALLEL" }, { "from": 432, "to": 434, "label": "EVAL with clause\nlog2(s(s(X227)), X228, X229, X230) :- log2(X227, s(X228), X229, X230).\nand substitutionX227 -> T138,\nT116 -> s(s(T138)),\nT119 -> T136,\nX228 -> s(T136),\nX229 -> s(0),\nT115 -> T137,\nX230 -> T137,\nT135 -> T138" }, { "from": 432, "to": 464, "label": "EVAL-BACKTRACK" }, { "from": 433, "to": 478, "label": "PARALLEL" }, { "from": 433, "to": 479, "label": "PARALLEL" }, { "from": 434, "to": 430, "label": "INSTANCE with matching:\nT116 -> T138\nT119 -> s(T136)\nT115 -> T137" }, { "from": 478, "to": 481, "label": "EVAL with clause\nlog2(X251, s(s(X252)), X253, X254) :- ','(small(X251), log2(X252, s(0), s(X253), X254)).\nand substitutionT116 -> T157,\nX251 -> T157,\nX252 -> T155,\nT119 -> s(T155),\nX253 -> s(0),\nT115 -> T156,\nX254 -> T156,\nT154 -> T157" }, { "from": 478, "to": 483, "label": "EVAL-BACKTRACK" }, { "from": 479, "to": 5695, "label": "EVAL with clause\nlog2(X4085, X4086, X4087, X4087) :- ','(small(X4085), small(X4086)).\nand substitutionT116 -> T1950,\nX4085 -> T1950,\nT119 -> T1949,\nX4086 -> s(T1949),\nX4087 -> s(0),\nT115 -> s(0),\nT1948 -> T1950" }, { "from": 479, "to": 5696, "label": "EVAL-BACKTRACK" }, { "from": 481, "to": 484, "label": "CASE" }, { "from": 484, "to": 485, "label": "PARALLEL" }, { "from": 484, "to": 486, "label": "PARALLEL" }, { "from": 485, "to": 487, "label": "EVAL with clause\nsmall(0).\nand substitutionT157 -> 0" }, { "from": 485, "to": 488, "label": "EVAL-BACKTRACK" }, { "from": 486, "to": 5662, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT157 -> s(0)" }, { "from": 486, "to": 5663, "label": "EVAL-BACKTRACK" }, { "from": 487, "to": 497, "label": "CASE" }, { "from": 497, "to": 499, "label": "PARALLEL" }, { "from": 497, "to": 500, "label": "PARALLEL" }, { "from": 499, "to": 503, "label": "EVAL with clause\nlog2(s(s(X279)), X280, X281, X282) :- log2(X279, s(X280), X281, X282).\nand substitutionX279 -> T170,\nT155 -> s(s(T170)),\nX280 -> s(0),\nX281 -> s(s(0)),\nT156 -> T171,\nX282 -> T171" }, { "from": 499, "to": 504, "label": "EVAL-BACKTRACK" }, { "from": 500, "to": 5635, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 503, "to": 507, "label": "CASE" }, { "from": 507, "to": 513, "label": "PARALLEL" }, { "from": 507, "to": 514, "label": "PARALLEL" }, { "from": 513, "to": 526, "label": "EVAL with clause\nlog2(s(s(X303)), X304, X305, X306) :- log2(X303, s(X304), X305, X306).\nand substitutionX303 -> T182,\nT170 -> s(s(T182)),\nX304 -> s(s(0)),\nX305 -> s(s(0)),\nT171 -> T183,\nX306 -> T183" }, { "from": 513, "to": 527, "label": "EVAL-BACKTRACK" }, { "from": 514, "to": 5546, "label": "PARALLEL" }, { "from": 514, "to": 5547, "label": "PARALLEL" }, { "from": 526, "to": 531, "label": "CASE" }, { "from": 531, "to": 532, "label": "PARALLEL" }, { "from": 531, "to": 533, "label": "PARALLEL" }, { "from": 532, "to": 543, "label": "EVAL with clause\nlog2(s(s(X327)), X328, X329, X330) :- log2(X327, s(X328), X329, X330).\nand substitutionX327 -> T194,\nT182 -> s(s(T194)),\nX328 -> s(s(s(0))),\nX329 -> s(s(0)),\nT183 -> T195,\nX330 -> T195" }, { "from": 532, "to": 544, "label": "EVAL-BACKTRACK" }, { "from": 533, "to": 5470, "label": "PARALLEL" }, { "from": 533, "to": 5471, "label": "PARALLEL" }, { "from": 543, "to": 545, "label": "CASE" }, { "from": 545, "to": 548, "label": "PARALLEL" }, { "from": 545, "to": 549, "label": "PARALLEL" }, { "from": 548, "to": 550, "label": "EVAL with clause\nlog2(s(s(X351)), X352, X353, X354) :- log2(X351, s(X352), X353, X354).\nand substitutionX351 -> T206,\nT194 -> s(s(T206)),\nX352 -> s(s(s(s(0)))),\nX353 -> s(s(0)),\nT195 -> T207,\nX354 -> T207" }, { "from": 548, "to": 551, "label": "EVAL-BACKTRACK" }, { "from": 549, "to": 5395, "label": "PARALLEL" }, { "from": 549, "to": 5396, "label": "PARALLEL" }, { "from": 550, "to": 555, "label": "CASE" }, { "from": 555, "to": 565, "label": "PARALLEL" }, { "from": 555, "to": 566, "label": "PARALLEL" }, { "from": 565, "to": 567, "label": "EVAL with clause\nlog2(s(s(X375)), X376, X377, X378) :- log2(X375, s(X376), X377, X378).\nand substitutionX375 -> T218,\nT206 -> s(s(T218)),\nX376 -> s(s(s(s(s(0))))),\nX377 -> s(s(0)),\nT207 -> T219,\nX378 -> T219" }, { "from": 565, "to": 568, "label": "EVAL-BACKTRACK" }, { "from": 566, "to": 5320, "label": "PARALLEL" }, { "from": 566, "to": 5321, "label": "PARALLEL" }, { "from": 567, "to": 571, "label": "CASE" }, { "from": 571, "to": 572, "label": "PARALLEL" }, { "from": 571, "to": 573, "label": "PARALLEL" }, { "from": 572, "to": 577, "label": "EVAL with clause\nlog2(s(s(X399)), X400, X401, X402) :- log2(X399, s(X400), X401, X402).\nand substitutionX399 -> T230,\nT218 -> s(s(T230)),\nX400 -> s(s(s(s(s(s(0)))))),\nX401 -> s(s(0)),\nT219 -> T231,\nX402 -> T231" }, { "from": 572, "to": 578, "label": "EVAL-BACKTRACK" }, { "from": 573, "to": 5245, "label": "PARALLEL" }, { "from": 573, "to": 5246, "label": "PARALLEL" }, { "from": 577, "to": 579, "label": "CASE" }, { "from": 579, "to": 582, "label": "PARALLEL" }, { "from": 579, "to": 583, "label": "PARALLEL" }, { "from": 582, "to": 585, "label": "EVAL with clause\nlog2(s(s(X423)), X424, X425, X426) :- log2(X423, s(X424), X425, X426).\nand substitutionX423 -> T242,\nT230 -> s(s(T242)),\nX424 -> s(s(s(s(s(s(s(0))))))),\nX425 -> s(s(0)),\nT231 -> T243,\nX426 -> T243" }, { "from": 582, "to": 586, "label": "EVAL-BACKTRACK" }, { "from": 583, "to": 5166, "label": "PARALLEL" }, { "from": 583, "to": 5167, "label": "PARALLEL" }, { "from": 585, "to": 589, "label": "GENERALIZATION\nT246 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT246 is ground" }, { "from": 589, "to": 592, "label": "CASE" }, { "from": 592, "to": 593, "label": "PARALLEL" }, { "from": 592, "to": 594, "label": "PARALLEL" }, { "from": 593, "to": 598, "label": "EVAL with clause\nlog2(s(s(X451)), X452, X453, X454) :- log2(X451, s(X452), X453, X454).\nand substitutionX451 -> T262,\nT242 -> s(s(T262)),\nT246 -> T263,\nX452 -> s(T263),\nX453 -> s(s(0)),\nT243 -> T264,\nX454 -> T264" }, { "from": 593, "to": 599, "label": "EVAL-BACKTRACK" }, { "from": 594, "to": 645, "label": "PARALLEL" }, { "from": 594, "to": 647, "label": "PARALLEL" }, { "from": 598, "to": 589, "label": "INSTANCE with matching:\nT242 -> T262\nT246 -> s(T263)\nT243 -> T264" }, { "from": 645, "to": 648, "label": "EVAL with clause\nlog2(X475, s(s(X476)), X477, X478) :- ','(small(X475), log2(X476, s(0), s(X477), X478)).\nand substitutionT242 -> T280,\nX475 -> T280,\nX476 -> T281,\nT246 -> s(T281),\nX477 -> s(s(0)),\nT243 -> T282,\nX478 -> T282" }, { "from": 645, "to": 649, "label": "EVAL-BACKTRACK" }, { "from": 647, "to": 5113, "label": "EVAL with clause\nlog2(X3765, X3766, X3767, X3767) :- ','(small(X3765), small(X3766)).\nand substitutionT242 -> T1838,\nX3765 -> T1838,\nT246 -> T1839,\nX3766 -> s(T1839),\nX3767 -> s(s(0)),\nT243 -> s(s(0))" }, { "from": 647, "to": 5114, "label": "EVAL-BACKTRACK" }, { "from": 648, "to": 652, "label": "CASE" }, { "from": 652, "to": 653, "label": "PARALLEL" }, { "from": 652, "to": 654, "label": "PARALLEL" }, { "from": 653, "to": 655, "label": "EVAL with clause\nsmall(0).\nand substitutionT280 -> 0" }, { "from": 653, "to": 656, "label": "EVAL-BACKTRACK" }, { "from": 654, "to": 5093, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT280 -> s(0)" }, { "from": 654, "to": 5094, "label": "EVAL-BACKTRACK" }, { "from": 655, "to": 662, "label": "CASE" }, { "from": 662, "to": 664, "label": "PARALLEL" }, { "from": 662, "to": 665, "label": "PARALLEL" }, { "from": 664, "to": 668, "label": "EVAL with clause\nlog2(s(s(X503)), X504, X505, X506) :- log2(X503, s(X504), X505, X506).\nand substitutionX503 -> T295,\nT281 -> s(s(T295)),\nX504 -> s(0),\nX505 -> s(s(s(0))),\nT282 -> T296,\nX506 -> T296" }, { "from": 664, "to": 669, "label": "EVAL-BACKTRACK" }, { "from": 665, "to": 5062, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 668, "to": 670, "label": "CASE" }, { "from": 670, "to": 673, "label": "PARALLEL" }, { "from": 670, "to": 674, "label": "PARALLEL" }, { "from": 673, "to": 693, "label": "EVAL with clause\nlog2(s(s(X527)), X528, X529, X530) :- log2(X527, s(X528), X529, X530).\nand substitutionX527 -> T307,\nT295 -> s(s(T307)),\nX528 -> s(s(0)),\nX529 -> s(s(s(0))),\nT296 -> T308,\nX530 -> T308" }, { "from": 673, "to": 694, "label": "EVAL-BACKTRACK" }, { "from": 674, "to": 4998, "label": "PARALLEL" }, { "from": 674, "to": 4999, "label": "PARALLEL" }, { "from": 693, "to": 696, "label": "CASE" }, { "from": 696, "to": 699, "label": "PARALLEL" }, { "from": 696, "to": 700, "label": "PARALLEL" }, { "from": 699, "to": 703, "label": "EVAL with clause\nlog2(s(s(X551)), X552, X553, X554) :- log2(X551, s(X552), X553, X554).\nand substitutionX551 -> T319,\nT307 -> s(s(T319)),\nX552 -> s(s(s(0))),\nX553 -> s(s(s(0))),\nT308 -> T320,\nX554 -> T320" }, { "from": 699, "to": 704, "label": "EVAL-BACKTRACK" }, { "from": 700, "to": 4903, "label": "PARALLEL" }, { "from": 700, "to": 4904, "label": "PARALLEL" }, { "from": 703, "to": 708, "label": "CASE" }, { "from": 708, "to": 710, "label": "PARALLEL" }, { "from": 708, "to": 711, "label": "PARALLEL" }, { "from": 710, "to": 715, "label": "EVAL with clause\nlog2(s(s(X575)), X576, X577, X578) :- log2(X575, s(X576), X577, X578).\nand substitutionX575 -> T331,\nT319 -> s(s(T331)),\nX576 -> s(s(s(s(0)))),\nX577 -> s(s(s(0))),\nT320 -> T332,\nX578 -> T332" }, { "from": 710, "to": 716, "label": "EVAL-BACKTRACK" }, { "from": 711, "to": 4828, "label": "PARALLEL" }, { "from": 711, "to": 4829, "label": "PARALLEL" }, { "from": 715, "to": 718, "label": "CASE" }, { "from": 718, "to": 720, "label": "PARALLEL" }, { "from": 718, "to": 721, "label": "PARALLEL" }, { "from": 720, "to": 728, "label": "EVAL with clause\nlog2(s(s(X599)), X600, X601, X602) :- log2(X599, s(X600), X601, X602).\nand substitutionX599 -> T343,\nT331 -> s(s(T343)),\nX600 -> s(s(s(s(s(0))))),\nX601 -> s(s(s(0))),\nT332 -> T344,\nX602 -> T344" }, { "from": 720, "to": 729, "label": "EVAL-BACKTRACK" }, { "from": 721, "to": 4753, "label": "PARALLEL" }, { "from": 721, "to": 4754, "label": "PARALLEL" }, { "from": 728, "to": 730, "label": "CASE" }, { "from": 730, "to": 731, "label": "PARALLEL" }, { "from": 730, "to": 732, "label": "PARALLEL" }, { "from": 731, "to": 733, "label": "EVAL with clause\nlog2(s(s(X623)), X624, X625, X626) :- log2(X623, s(X624), X625, X626).\nand substitutionX623 -> T355,\nT343 -> s(s(T355)),\nX624 -> s(s(s(s(s(s(0)))))),\nX625 -> s(s(s(0))),\nT344 -> T356,\nX626 -> T356" }, { "from": 731, "to": 735, "label": "EVAL-BACKTRACK" }, { "from": 732, "to": 4678, "label": "PARALLEL" }, { "from": 732, "to": 4679, "label": "PARALLEL" }, { "from": 733, "to": 740, "label": "CASE" }, { "from": 740, "to": 743, "label": "PARALLEL" }, { "from": 740, "to": 744, "label": "PARALLEL" }, { "from": 743, "to": 748, "label": "EVAL with clause\nlog2(s(s(X647)), X648, X649, X650) :- log2(X647, s(X648), X649, X650).\nand substitutionX647 -> T367,\nT355 -> s(s(T367)),\nX648 -> s(s(s(s(s(s(s(0))))))),\nX649 -> s(s(s(0))),\nT356 -> T368,\nX650 -> T368" }, { "from": 743, "to": 749, "label": "EVAL-BACKTRACK" }, { "from": 744, "to": 4582, "label": "PARALLEL" }, { "from": 744, "to": 4583, "label": "PARALLEL" }, { "from": 748, "to": 752, "label": "GENERALIZATION\nT371 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT371 is ground" }, { "from": 752, "to": 754, "label": "CASE" }, { "from": 754, "to": 757, "label": "PARALLEL" }, { "from": 754, "to": 758, "label": "PARALLEL" }, { "from": 757, "to": 763, "label": "EVAL with clause\nlog2(s(s(X675)), X676, X677, X678) :- log2(X675, s(X676), X677, X678).\nand substitutionX675 -> T387,\nT367 -> s(s(T387)),\nT371 -> T388,\nX676 -> s(T388),\nX677 -> s(s(s(0))),\nT368 -> T389,\nX678 -> T389" }, { "from": 757, "to": 764, "label": "EVAL-BACKTRACK" }, { "from": 758, "to": 771, "label": "PARALLEL" }, { "from": 758, "to": 772, "label": "PARALLEL" }, { "from": 763, "to": 752, "label": "INSTANCE with matching:\nT367 -> T387\nT371 -> s(T388)\nT368 -> T389" }, { "from": 771, "to": 779, "label": "EVAL with clause\nlog2(X699, s(s(X700)), X701, X702) :- ','(small(X699), log2(X700, s(0), s(X701), X702)).\nand substitutionT367 -> T405,\nX699 -> T405,\nX700 -> T406,\nT371 -> s(T406),\nX701 -> s(s(s(0))),\nT368 -> T407,\nX702 -> T407" }, { "from": 771, "to": 780, "label": "EVAL-BACKTRACK" }, { "from": 772, "to": 4545, "label": "EVAL with clause\nlog2(X3445, X3446, X3447, X3447) :- ','(small(X3445), small(X3446)).\nand substitutionT367 -> T1728,\nX3445 -> T1728,\nT371 -> T1729,\nX3446 -> s(T1729),\nX3447 -> s(s(s(0))),\nT368 -> s(s(s(0)))" }, { "from": 772, "to": 4546, "label": "EVAL-BACKTRACK" }, { "from": 779, "to": 782, "label": "CASE" }, { "from": 782, "to": 784, "label": "PARALLEL" }, { "from": 782, "to": 785, "label": "PARALLEL" }, { "from": 784, "to": 786, "label": "EVAL with clause\nsmall(0).\nand substitutionT405 -> 0" }, { "from": 784, "to": 787, "label": "EVAL-BACKTRACK" }, { "from": 785, "to": 4521, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT405 -> s(0)" }, { "from": 785, "to": 4522, "label": "EVAL-BACKTRACK" }, { "from": 786, "to": 791, "label": "CASE" }, { "from": 791, "to": 794, "label": "PARALLEL" }, { "from": 791, "to": 795, "label": "PARALLEL" }, { "from": 794, "to": 800, "label": "EVAL with clause\nlog2(s(s(X727)), X728, X729, X730) :- log2(X727, s(X728), X729, X730).\nand substitutionX727 -> T420,\nT406 -> s(s(T420)),\nX728 -> s(0),\nX729 -> s(s(s(s(0)))),\nT407 -> T421,\nX730 -> T421" }, { "from": 794, "to": 801, "label": "EVAL-BACKTRACK" }, { "from": 795, "to": 4500, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 800, "to": 805, "label": "CASE" }, { "from": 805, "to": 806, "label": "PARALLEL" }, { "from": 805, "to": 807, "label": "PARALLEL" }, { "from": 806, "to": 811, "label": "EVAL with clause\nlog2(s(s(X751)), X752, X753, X754) :- log2(X751, s(X752), X753, X754).\nand substitutionX751 -> T432,\nT420 -> s(s(T432)),\nX752 -> s(s(0)),\nX753 -> s(s(s(s(0)))),\nT421 -> T433,\nX754 -> T433" }, { "from": 806, "to": 812, "label": "EVAL-BACKTRACK" }, { "from": 807, "to": 4423, "label": "PARALLEL" }, { "from": 807, "to": 4424, "label": "PARALLEL" }, { "from": 811, "to": 815, "label": "CASE" }, { "from": 815, "to": 819, "label": "PARALLEL" }, { "from": 815, "to": 820, "label": "PARALLEL" }, { "from": 819, "to": 825, "label": "EVAL with clause\nlog2(s(s(X775)), X776, X777, X778) :- log2(X775, s(X776), X777, X778).\nand substitutionX775 -> T444,\nT432 -> s(s(T444)),\nX776 -> s(s(s(0))),\nX777 -> s(s(s(s(0)))),\nT433 -> T445,\nX778 -> T445" }, { "from": 819, "to": 826, "label": "EVAL-BACKTRACK" }, { "from": 820, "to": 4330, "label": "PARALLEL" }, { "from": 820, "to": 4331, "label": "PARALLEL" }, { "from": 825, "to": 850, "label": "CASE" }, { "from": 850, "to": 862, "label": "PARALLEL" }, { "from": 850, "to": 863, "label": "PARALLEL" }, { "from": 862, "to": 866, "label": "EVAL with clause\nlog2(s(s(X799)), X800, X801, X802) :- log2(X799, s(X800), X801, X802).\nand substitutionX799 -> T456,\nT444 -> s(s(T456)),\nX800 -> s(s(s(s(0)))),\nX801 -> s(s(s(s(0)))),\nT445 -> T457,\nX802 -> T457" }, { "from": 862, "to": 867, "label": "EVAL-BACKTRACK" }, { "from": 863, "to": 4255, "label": "PARALLEL" }, { "from": 863, "to": 4256, "label": "PARALLEL" }, { "from": 866, "to": 870, "label": "CASE" }, { "from": 870, "to": 872, "label": "PARALLEL" }, { "from": 870, "to": 873, "label": "PARALLEL" }, { "from": 872, "to": 883, "label": "EVAL with clause\nlog2(s(s(X823)), X824, X825, X826) :- log2(X823, s(X824), X825, X826).\nand substitutionX823 -> T468,\nT456 -> s(s(T468)),\nX824 -> s(s(s(s(s(0))))),\nX825 -> s(s(s(s(0)))),\nT457 -> T469,\nX826 -> T469" }, { "from": 872, "to": 884, "label": "EVAL-BACKTRACK" }, { "from": 873, "to": 4176, "label": "PARALLEL" }, { "from": 873, "to": 4177, "label": "PARALLEL" }, { "from": 883, "to": 885, "label": "CASE" }, { "from": 885, "to": 886, "label": "PARALLEL" }, { "from": 885, "to": 887, "label": "PARALLEL" }, { "from": 886, "to": 888, "label": "EVAL with clause\nlog2(s(s(X847)), X848, X849, X850) :- log2(X847, s(X848), X849, X850).\nand substitutionX847 -> T480,\nT468 -> s(s(T480)),\nX848 -> s(s(s(s(s(s(0)))))),\nX849 -> s(s(s(s(0)))),\nT469 -> T481,\nX850 -> T481" }, { "from": 886, "to": 889, "label": "EVAL-BACKTRACK" }, { "from": 887, "to": 4082, "label": "PARALLEL" }, { "from": 887, "to": 4083, "label": "PARALLEL" }, { "from": 888, "to": 892, "label": "CASE" }, { "from": 892, "to": 894, "label": "PARALLEL" }, { "from": 892, "to": 895, "label": "PARALLEL" }, { "from": 894, "to": 898, "label": "EVAL with clause\nlog2(s(s(X871)), X872, X873, X874) :- log2(X871, s(X872), X873, X874).\nand substitutionX871 -> T492,\nT480 -> s(s(T492)),\nX872 -> s(s(s(s(s(s(s(0))))))),\nX873 -> s(s(s(s(0)))),\nT481 -> T493,\nX874 -> T493" }, { "from": 894, "to": 899, "label": "EVAL-BACKTRACK" }, { "from": 895, "to": 3989, "label": "PARALLEL" }, { "from": 895, "to": 3990, "label": "PARALLEL" }, { "from": 898, "to": 902, "label": "GENERALIZATION\nT496 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT496 is ground" }, { "from": 902, "to": 904, "label": "CASE" }, { "from": 904, "to": 907, "label": "PARALLEL" }, { "from": 904, "to": 908, "label": "PARALLEL" }, { "from": 907, "to": 910, "label": "EVAL with clause\nlog2(s(s(X899)), X900, X901, X902) :- log2(X899, s(X900), X901, X902).\nand substitutionX899 -> T512,\nT492 -> s(s(T512)),\nT496 -> T513,\nX900 -> s(T513),\nX901 -> s(s(s(s(0)))),\nT493 -> T514,\nX902 -> T514" }, { "from": 907, "to": 911, "label": "EVAL-BACKTRACK" }, { "from": 908, "to": 918, "label": "PARALLEL" }, { "from": 908, "to": 919, "label": "PARALLEL" }, { "from": 910, "to": 902, "label": "INSTANCE with matching:\nT492 -> T512\nT496 -> s(T513)\nT493 -> T514" }, { "from": 918, "to": 924, "label": "EVAL with clause\nlog2(X923, s(s(X924)), X925, X926) :- ','(small(X923), log2(X924, s(0), s(X925), X926)).\nand substitutionT492 -> T530,\nX923 -> T530,\nX924 -> T531,\nT496 -> s(T531),\nX925 -> s(s(s(s(0)))),\nT493 -> T532,\nX926 -> T532" }, { "from": 918, "to": 925, "label": "EVAL-BACKTRACK" }, { "from": 919, "to": 3953, "label": "EVAL with clause\nlog2(X3125, X3126, X3127, X3127) :- ','(small(X3125), small(X3126)).\nand substitutionT492 -> T1618,\nX3125 -> T1618,\nT496 -> T1619,\nX3126 -> s(T1619),\nX3127 -> s(s(s(s(0)))),\nT493 -> s(s(s(s(0))))" }, { "from": 919, "to": 3954, "label": "EVAL-BACKTRACK" }, { "from": 924, "to": 928, "label": "CASE" }, { "from": 928, "to": 929, "label": "PARALLEL" }, { "from": 928, "to": 930, "label": "PARALLEL" }, { "from": 929, "to": 931, "label": "EVAL with clause\nsmall(0).\nand substitutionT530 -> 0" }, { "from": 929, "to": 932, "label": "EVAL-BACKTRACK" }, { "from": 930, "to": 3918, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT530 -> s(0)" }, { "from": 930, "to": 3919, "label": "EVAL-BACKTRACK" }, { "from": 931, "to": 945, "label": "CASE" }, { "from": 945, "to": 950, "label": "PARALLEL" }, { "from": 945, "to": 951, "label": "PARALLEL" }, { "from": 950, "to": 957, "label": "EVAL with clause\nlog2(s(s(X951)), X952, X953, X954) :- log2(X951, s(X952), X953, X954).\nand substitutionX951 -> T545,\nT531 -> s(s(T545)),\nX952 -> s(0),\nX953 -> s(s(s(s(s(0))))),\nT532 -> T546,\nX954 -> T546" }, { "from": 950, "to": 958, "label": "EVAL-BACKTRACK" }, { "from": 951, "to": 3850, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 957, "to": 972, "label": "CASE" }, { "from": 972, "to": 976, "label": "PARALLEL" }, { "from": 972, "to": 977, "label": "PARALLEL" }, { "from": 976, "to": 982, "label": "EVAL with clause\nlog2(s(s(X975)), X976, X977, X978) :- log2(X975, s(X976), X977, X978).\nand substitutionX975 -> T557,\nT545 -> s(s(T557)),\nX976 -> s(s(0)),\nX977 -> s(s(s(s(s(0))))),\nT546 -> T558,\nX978 -> T558" }, { "from": 976, "to": 983, "label": "EVAL-BACKTRACK" }, { "from": 977, "to": 3772, "label": "PARALLEL" }, { "from": 977, "to": 3773, "label": "PARALLEL" }, { "from": 982, "to": 986, "label": "CASE" }, { "from": 986, "to": 988, "label": "PARALLEL" }, { "from": 986, "to": 989, "label": "PARALLEL" }, { "from": 988, "to": 994, "label": "EVAL with clause\nlog2(s(s(X999)), X1000, X1001, X1002) :- log2(X999, s(X1000), X1001, X1002).\nand substitutionX999 -> T569,\nT557 -> s(s(T569)),\nX1000 -> s(s(s(0))),\nX1001 -> s(s(s(s(s(0))))),\nT558 -> T570,\nX1002 -> T570" }, { "from": 988, "to": 995, "label": "EVAL-BACKTRACK" }, { "from": 989, "to": 3736, "label": "PARALLEL" }, { "from": 989, "to": 3737, "label": "PARALLEL" }, { "from": 994, "to": 998, "label": "CASE" }, { "from": 998, "to": 1000, "label": "PARALLEL" }, { "from": 998, "to": 1001, "label": "PARALLEL" }, { "from": 1000, "to": 1004, "label": "EVAL with clause\nlog2(s(s(X1023)), X1024, X1025, X1026) :- log2(X1023, s(X1024), X1025, X1026).\nand substitutionX1023 -> T581,\nT569 -> s(s(T581)),\nX1024 -> s(s(s(s(0)))),\nX1025 -> s(s(s(s(s(0))))),\nT570 -> T582,\nX1026 -> T582" }, { "from": 1000, "to": 1005, "label": "EVAL-BACKTRACK" }, { "from": 1001, "to": 3677, "label": "PARALLEL" }, { "from": 1001, "to": 3678, "label": "PARALLEL" }, { "from": 1004, "to": 1008, "label": "CASE" }, { "from": 1008, "to": 1010, "label": "PARALLEL" }, { "from": 1008, "to": 1011, "label": "PARALLEL" }, { "from": 1010, "to": 1014, "label": "EVAL with clause\nlog2(s(s(X1047)), X1048, X1049, X1050) :- log2(X1047, s(X1048), X1049, X1050).\nand substitutionX1047 -> T593,\nT581 -> s(s(T593)),\nX1048 -> s(s(s(s(s(0))))),\nX1049 -> s(s(s(s(s(0))))),\nT582 -> T594,\nX1050 -> T594" }, { "from": 1010, "to": 1015, "label": "EVAL-BACKTRACK" }, { "from": 1011, "to": 3547, "label": "PARALLEL" }, { "from": 1011, "to": 3548, "label": "PARALLEL" }, { "from": 1014, "to": 1031, "label": "CASE" }, { "from": 1031, "to": 1032, "label": "PARALLEL" }, { "from": 1031, "to": 1033, "label": "PARALLEL" }, { "from": 1032, "to": 1036, "label": "EVAL with clause\nlog2(s(s(X1071)), X1072, X1073, X1074) :- log2(X1071, s(X1072), X1073, X1074).\nand substitutionX1071 -> T605,\nT593 -> s(s(T605)),\nX1072 -> s(s(s(s(s(s(0)))))),\nX1073 -> s(s(s(s(s(0))))),\nT594 -> T606,\nX1074 -> T606" }, { "from": 1032, "to": 1037, "label": "EVAL-BACKTRACK" }, { "from": 1033, "to": 3428, "label": "PARALLEL" }, { "from": 1033, "to": 3429, "label": "PARALLEL" }, { "from": 1036, "to": 1038, "label": "CASE" }, { "from": 1038, "to": 1039, "label": "PARALLEL" }, { "from": 1038, "to": 1040, "label": "PARALLEL" }, { "from": 1039, "to": 1041, "label": "EVAL with clause\nlog2(s(s(X1095)), X1096, X1097, X1098) :- log2(X1095, s(X1096), X1097, X1098).\nand substitutionX1095 -> T617,\nT605 -> s(s(T617)),\nX1096 -> s(s(s(s(s(s(s(0))))))),\nX1097 -> s(s(s(s(s(0))))),\nT606 -> T618,\nX1098 -> T618" }, { "from": 1039, "to": 1042, "label": "EVAL-BACKTRACK" }, { "from": 1040, "to": 3358, "label": "PARALLEL" }, { "from": 1040, "to": 3359, "label": "PARALLEL" }, { "from": 1041, "to": 1045, "label": "GENERALIZATION\nT621 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT621 is ground" }, { "from": 1045, "to": 1051, "label": "CASE" }, { "from": 1051, "to": 1053, "label": "PARALLEL" }, { "from": 1051, "to": 1054, "label": "PARALLEL" }, { "from": 1053, "to": 1065, "label": "EVAL with clause\nlog2(s(s(X1123)), X1124, X1125, X1126) :- log2(X1123, s(X1124), X1125, X1126).\nand substitutionX1123 -> T637,\nT617 -> s(s(T637)),\nT621 -> T638,\nX1124 -> s(T638),\nX1125 -> s(s(s(s(s(0))))),\nT618 -> T639,\nX1126 -> T639" }, { "from": 1053, "to": 1066, "label": "EVAL-BACKTRACK" }, { "from": 1054, "to": 1077, "label": "PARALLEL" }, { "from": 1054, "to": 1078, "label": "PARALLEL" }, { "from": 1065, "to": 1045, "label": "INSTANCE with matching:\nT617 -> T637\nT621 -> s(T638)\nT618 -> T639" }, { "from": 1077, "to": 1084, "label": "EVAL with clause\nlog2(X1147, s(s(X1148)), X1149, X1150) :- ','(small(X1147), log2(X1148, s(0), s(X1149), X1150)).\nand substitutionT617 -> T655,\nX1147 -> T655,\nX1148 -> T656,\nT621 -> s(T656),\nX1149 -> s(s(s(s(s(0))))),\nT618 -> T657,\nX1150 -> T657" }, { "from": 1077, "to": 1085, "label": "EVAL-BACKTRACK" }, { "from": 1078, "to": 3337, "label": "EVAL with clause\nlog2(X2805, X2806, X2807, X2807) :- ','(small(X2805), small(X2806)).\nand substitutionT617 -> T1508,\nX2805 -> T1508,\nT621 -> T1509,\nX2806 -> s(T1509),\nX2807 -> s(s(s(s(s(0))))),\nT618 -> s(s(s(s(s(0)))))" }, { "from": 1078, "to": 3338, "label": "EVAL-BACKTRACK" }, { "from": 1084, "to": 1091, "label": "CASE" }, { "from": 1091, "to": 1092, "label": "PARALLEL" }, { "from": 1091, "to": 1093, "label": "PARALLEL" }, { "from": 1092, "to": 1094, "label": "EVAL with clause\nsmall(0).\nand substitutionT655 -> 0" }, { "from": 1092, "to": 1095, "label": "EVAL-BACKTRACK" }, { "from": 1093, "to": 3318, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT655 -> s(0)" }, { "from": 1093, "to": 3319, "label": "EVAL-BACKTRACK" }, { "from": 1094, "to": 1121, "label": "CASE" }, { "from": 1121, "to": 1129, "label": "PARALLEL" }, { "from": 1121, "to": 1130, "label": "PARALLEL" }, { "from": 1129, "to": 1134, "label": "EVAL with clause\nlog2(s(s(X1175)), X1176, X1177, X1178) :- log2(X1175, s(X1176), X1177, X1178).\nand substitutionX1175 -> T670,\nT656 -> s(s(T670)),\nX1176 -> s(0),\nX1177 -> s(s(s(s(s(s(0)))))),\nT657 -> T671,\nX1178 -> T671" }, { "from": 1129, "to": 1136, "label": "EVAL-BACKTRACK" }, { "from": 1130, "to": 3234, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1134, "to": 1138, "label": "CASE" }, { "from": 1138, "to": 1140, "label": "PARALLEL" }, { "from": 1138, "to": 1141, "label": "PARALLEL" }, { "from": 1140, "to": 1142, "label": "EVAL with clause\nlog2(s(s(X1199)), X1200, X1201, X1202) :- log2(X1199, s(X1200), X1201, X1202).\nand substitutionX1199 -> T682,\nT670 -> s(s(T682)),\nX1200 -> s(s(0)),\nX1201 -> s(s(s(s(s(s(0)))))),\nT671 -> T683,\nX1202 -> T683" }, { "from": 1140, "to": 1143, "label": "EVAL-BACKTRACK" }, { "from": 1141, "to": 3167, "label": "PARALLEL" }, { "from": 1141, "to": 3168, "label": "PARALLEL" }, { "from": 1142, "to": 1147, "label": "CASE" }, { "from": 1147, "to": 1150, "label": "PARALLEL" }, { "from": 1147, "to": 1151, "label": "PARALLEL" }, { "from": 1150, "to": 1154, "label": "EVAL with clause\nlog2(s(s(X1223)), X1224, X1225, X1226) :- log2(X1223, s(X1224), X1225, X1226).\nand substitutionX1223 -> T694,\nT682 -> s(s(T694)),\nX1224 -> s(s(s(0))),\nX1225 -> s(s(s(s(s(s(0)))))),\nT683 -> T695,\nX1226 -> T695" }, { "from": 1150, "to": 1155, "label": "EVAL-BACKTRACK" }, { "from": 1151, "to": 3036, "label": "PARALLEL" }, { "from": 1151, "to": 3037, "label": "PARALLEL" }, { "from": 1154, "to": 1157, "label": "CASE" }, { "from": 1157, "to": 1160, "label": "PARALLEL" }, { "from": 1157, "to": 1161, "label": "PARALLEL" }, { "from": 1160, "to": 1165, "label": "EVAL with clause\nlog2(s(s(X1247)), X1248, X1249, X1250) :- log2(X1247, s(X1248), X1249, X1250).\nand substitutionX1247 -> T706,\nT694 -> s(s(T706)),\nX1248 -> s(s(s(s(0)))),\nX1249 -> s(s(s(s(s(s(0)))))),\nT695 -> T707,\nX1250 -> T707" }, { "from": 1160, "to": 1166, "label": "EVAL-BACKTRACK" }, { "from": 1161, "to": 2935, "label": "PARALLEL" }, { "from": 1161, "to": 2936, "label": "PARALLEL" }, { "from": 1165, "to": 1167, "label": "CASE" }, { "from": 1167, "to": 1168, "label": "PARALLEL" }, { "from": 1167, "to": 1169, "label": "PARALLEL" }, { "from": 1168, "to": 1172, "label": "EVAL with clause\nlog2(s(s(X1271)), X1272, X1273, X1274) :- log2(X1271, s(X1272), X1273, X1274).\nand substitutionX1271 -> T718,\nT706 -> s(s(T718)),\nX1272 -> s(s(s(s(s(0))))),\nX1273 -> s(s(s(s(s(s(0)))))),\nT707 -> T719,\nX1274 -> T719" }, { "from": 1168, "to": 1173, "label": "EVAL-BACKTRACK" }, { "from": 1169, "to": 2840, "label": "PARALLEL" }, { "from": 1169, "to": 2841, "label": "PARALLEL" }, { "from": 1172, "to": 1186, "label": "CASE" }, { "from": 1186, "to": 1201, "label": "PARALLEL" }, { "from": 1186, "to": 1202, "label": "PARALLEL" }, { "from": 1201, "to": 1209, "label": "EVAL with clause\nlog2(s(s(X1295)), X1296, X1297, X1298) :- log2(X1295, s(X1296), X1297, X1298).\nand substitutionX1295 -> T730,\nT718 -> s(s(T730)),\nX1296 -> s(s(s(s(s(s(0)))))),\nX1297 -> s(s(s(s(s(s(0)))))),\nT719 -> T731,\nX1298 -> T731" }, { "from": 1201, "to": 1210, "label": "EVAL-BACKTRACK" }, { "from": 1202, "to": 2790, "label": "PARALLEL" }, { "from": 1202, "to": 2791, "label": "PARALLEL" }, { "from": 1209, "to": 1215, "label": "CASE" }, { "from": 1215, "to": 1220, "label": "PARALLEL" }, { "from": 1215, "to": 1221, "label": "PARALLEL" }, { "from": 1220, "to": 1238, "label": "EVAL with clause\nlog2(s(s(X1319)), X1320, X1321, X1322) :- log2(X1319, s(X1320), X1321, X1322).\nand substitutionX1319 -> T742,\nT730 -> s(s(T742)),\nX1320 -> s(s(s(s(s(s(s(0))))))),\nX1321 -> s(s(s(s(s(s(0)))))),\nT731 -> T743,\nX1322 -> T743" }, { "from": 1220, "to": 1239, "label": "EVAL-BACKTRACK" }, { "from": 1221, "to": 2645, "label": "PARALLEL" }, { "from": 1221, "to": 2646, "label": "PARALLEL" }, { "from": 1238, "to": 1241, "label": "GENERALIZATION\nT746 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT746 is ground" }, { "from": 1241, "to": 1259, "label": "CASE" }, { "from": 1259, "to": 1261, "label": "PARALLEL" }, { "from": 1259, "to": 1262, "label": "PARALLEL" }, { "from": 1261, "to": 1267, "label": "EVAL with clause\nlog2(s(s(X1347)), X1348, X1349, X1350) :- log2(X1347, s(X1348), X1349, X1350).\nand substitutionX1347 -> T762,\nT742 -> s(s(T762)),\nT746 -> T763,\nX1348 -> s(T763),\nX1349 -> s(s(s(s(s(s(0)))))),\nT743 -> T764,\nX1350 -> T764" }, { "from": 1261, "to": 1268, "label": "EVAL-BACKTRACK" }, { "from": 1262, "to": 1273, "label": "PARALLEL" }, { "from": 1262, "to": 1274, "label": "PARALLEL" }, { "from": 1267, "to": 1241, "label": "INSTANCE with matching:\nT742 -> T762\nT746 -> s(T763)\nT743 -> T764" }, { "from": 1273, "to": 1281, "label": "EVAL with clause\nlog2(X1371, s(s(X1372)), X1373, X1374) :- ','(small(X1371), log2(X1372, s(0), s(X1373), X1374)).\nand substitutionT742 -> T780,\nX1371 -> T780,\nX1372 -> T781,\nT746 -> s(T781),\nX1373 -> s(s(s(s(s(s(0)))))),\nT743 -> T782,\nX1374 -> T782" }, { "from": 1273, "to": 1282, "label": "EVAL-BACKTRACK" }, { "from": 1274, "to": 2610, "label": "EVAL with clause\nlog2(X2485, X2486, X2487, X2487) :- ','(small(X2485), small(X2486)).\nand substitutionT742 -> T1398,\nX2485 -> T1398,\nT746 -> T1399,\nX2486 -> s(T1399),\nX2487 -> s(s(s(s(s(s(0)))))),\nT743 -> s(s(s(s(s(s(0))))))" }, { "from": 1274, "to": 2611, "label": "EVAL-BACKTRACK" }, { "from": 1281, "to": 1283, "label": "CASE" }, { "from": 1283, "to": 1284, "label": "PARALLEL" }, { "from": 1283, "to": 1285, "label": "PARALLEL" }, { "from": 1284, "to": 1286, "label": "EVAL with clause\nsmall(0).\nand substitutionT780 -> 0" }, { "from": 1284, "to": 1288, "label": "EVAL-BACKTRACK" }, { "from": 1285, "to": 2591, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT780 -> s(0)" }, { "from": 1285, "to": 2592, "label": "EVAL-BACKTRACK" }, { "from": 1286, "to": 1290, "label": "CASE" }, { "from": 1290, "to": 1293, "label": "PARALLEL" }, { "from": 1290, "to": 1294, "label": "PARALLEL" }, { "from": 1293, "to": 1300, "label": "EVAL with clause\nlog2(s(s(X1399)), X1400, X1401, X1402) :- log2(X1399, s(X1400), X1401, X1402).\nand substitutionX1399 -> T795,\nT781 -> s(s(T795)),\nX1400 -> s(0),\nX1401 -> s(s(s(s(s(s(s(0))))))),\nT782 -> T796,\nX1402 -> T796" }, { "from": 1293, "to": 1301, "label": "EVAL-BACKTRACK" }, { "from": 1294, "to": 2569, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1300, "to": 1304, "label": "CASE" }, { "from": 1304, "to": 1305, "label": "PARALLEL" }, { "from": 1304, "to": 1306, "label": "PARALLEL" }, { "from": 1305, "to": 1307, "label": "EVAL with clause\nlog2(s(s(X1423)), X1424, X1425, X1426) :- log2(X1423, s(X1424), X1425, X1426).\nand substitutionX1423 -> T807,\nT795 -> s(s(T807)),\nX1424 -> s(s(0)),\nX1425 -> s(s(s(s(s(s(s(0))))))),\nT796 -> T808,\nX1426 -> T808" }, { "from": 1305, "to": 1308, "label": "EVAL-BACKTRACK" }, { "from": 1306, "to": 2481, "label": "PARALLEL" }, { "from": 1306, "to": 2483, "label": "PARALLEL" }, { "from": 1307, "to": 1309, "label": "CASE" }, { "from": 1309, "to": 1310, "label": "PARALLEL" }, { "from": 1309, "to": 1311, "label": "PARALLEL" }, { "from": 1310, "to": 1327, "label": "EVAL with clause\nlog2(s(s(X1447)), X1448, X1449, X1450) :- log2(X1447, s(X1448), X1449, X1450).\nand substitutionX1447 -> T819,\nT807 -> s(s(T819)),\nX1448 -> s(s(s(0))),\nX1449 -> s(s(s(s(s(s(s(0))))))),\nT808 -> T820,\nX1450 -> T820" }, { "from": 1310, "to": 1328, "label": "EVAL-BACKTRACK" }, { "from": 1311, "to": 2417, "label": "PARALLEL" }, { "from": 1311, "to": 2418, "label": "PARALLEL" }, { "from": 1327, "to": 1331, "label": "CASE" }, { "from": 1331, "to": 1332, "label": "PARALLEL" }, { "from": 1331, "to": 1333, "label": "PARALLEL" }, { "from": 1332, "to": 1338, "label": "EVAL with clause\nlog2(s(s(X1471)), X1472, X1473, X1474) :- log2(X1471, s(X1472), X1473, X1474).\nand substitutionX1471 -> T831,\nT819 -> s(s(T831)),\nX1472 -> s(s(s(s(0)))),\nX1473 -> s(s(s(s(s(s(s(0))))))),\nT820 -> T832,\nX1474 -> T832" }, { "from": 1332, "to": 1340, "label": "EVAL-BACKTRACK" }, { "from": 1333, "to": 2311, "label": "PARALLEL" }, { "from": 1333, "to": 2312, "label": "PARALLEL" }, { "from": 1338, "to": 1342, "label": "CASE" }, { "from": 1342, "to": 1343, "label": "PARALLEL" }, { "from": 1342, "to": 1344, "label": "PARALLEL" }, { "from": 1343, "to": 1376, "label": "EVAL with clause\nlog2(s(s(X1495)), X1496, X1497, X1498) :- log2(X1495, s(X1496), X1497, X1498).\nand substitutionX1495 -> T843,\nT831 -> s(s(T843)),\nX1496 -> s(s(s(s(s(0))))),\nX1497 -> s(s(s(s(s(s(s(0))))))),\nT832 -> T844,\nX1498 -> T844" }, { "from": 1343, "to": 1377, "label": "EVAL-BACKTRACK" }, { "from": 1344, "to": 2243, "label": "PARALLEL" }, { "from": 1344, "to": 2244, "label": "PARALLEL" }, { "from": 1376, "to": 1385, "label": "CASE" }, { "from": 1385, "to": 1390, "label": "PARALLEL" }, { "from": 1385, "to": 1391, "label": "PARALLEL" }, { "from": 1390, "to": 1392, "label": "EVAL with clause\nlog2(s(s(X1519)), X1520, X1521, X1522) :- log2(X1519, s(X1520), X1521, X1522).\nand substitutionX1519 -> T855,\nT843 -> s(s(T855)),\nX1520 -> s(s(s(s(s(s(0)))))),\nX1521 -> s(s(s(s(s(s(s(0))))))),\nT844 -> T856,\nX1522 -> T856" }, { "from": 1390, "to": 1393, "label": "EVAL-BACKTRACK" }, { "from": 1391, "to": 2125, "label": "PARALLEL" }, { "from": 1391, "to": 2126, "label": "PARALLEL" }, { "from": 1392, "to": 1395, "label": "CASE" }, { "from": 1395, "to": 1398, "label": "PARALLEL" }, { "from": 1395, "to": 1399, "label": "PARALLEL" }, { "from": 1398, "to": 1402, "label": "EVAL with clause\nlog2(s(s(X1543)), X1544, X1545, X1546) :- log2(X1543, s(X1544), X1545, X1546).\nand substitutionX1543 -> T867,\nT855 -> s(s(T867)),\nX1544 -> s(s(s(s(s(s(s(0))))))),\nX1545 -> s(s(s(s(s(s(s(0))))))),\nT856 -> T868,\nX1546 -> T868" }, { "from": 1398, "to": 1403, "label": "EVAL-BACKTRACK" }, { "from": 1399, "to": 2058, "label": "PARALLEL" }, { "from": 1399, "to": 2059, "label": "PARALLEL" }, { "from": 1402, "to": 1416, "label": "GENERALIZATION\nT871 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT871 is ground" }, { "from": 1416, "to": 1419, "label": "CASE" }, { "from": 1419, "to": 1421, "label": "PARALLEL" }, { "from": 1419, "to": 1422, "label": "PARALLEL" }, { "from": 1421, "to": 1425, "label": "EVAL with clause\nlog2(s(s(X1571)), X1572, X1573, X1574) :- log2(X1571, s(X1572), X1573, X1574).\nand substitutionX1571 -> T887,\nT867 -> s(s(T887)),\nT871 -> T888,\nX1572 -> s(T888),\nX1573 -> s(s(s(s(s(s(s(0))))))),\nT868 -> T889,\nX1574 -> T889" }, { "from": 1421, "to": 1426, "label": "EVAL-BACKTRACK" }, { "from": 1422, "to": 1427, "label": "PARALLEL" }, { "from": 1422, "to": 1428, "label": "PARALLEL" }, { "from": 1425, "to": 1416, "label": "INSTANCE with matching:\nT867 -> T887\nT871 -> s(T888)\nT868 -> T889" }, { "from": 1427, "to": 1429, "label": "EVAL with clause\nlog2(X1595, s(s(X1596)), X1597, X1598) :- ','(small(X1595), log2(X1596, s(0), s(X1597), X1598)).\nand substitutionT867 -> T905,\nX1595 -> T905,\nX1596 -> T906,\nT871 -> s(T906),\nX1597 -> s(s(s(s(s(s(s(0))))))),\nT868 -> T907,\nX1598 -> T907" }, { "from": 1427, "to": 1430, "label": "EVAL-BACKTRACK" }, { "from": 1428, "to": 2022, "label": "EVAL with clause\nlog2(X2165, X2166, X2167, X2167) :- ','(small(X2165), small(X2166)).\nand substitutionT867 -> T1288,\nX2165 -> T1288,\nT871 -> T1289,\nX2166 -> s(T1289),\nX2167 -> s(s(s(s(s(s(s(0))))))),\nT868 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 1428, "to": 2023, "label": "EVAL-BACKTRACK" }, { "from": 1429, "to": 1433, "label": "CASE" }, { "from": 1433, "to": 1434, "label": "PARALLEL" }, { "from": 1433, "to": 1435, "label": "PARALLEL" }, { "from": 1434, "to": 1436, "label": "EVAL with clause\nsmall(0).\nand substitutionT905 -> 0" }, { "from": 1434, "to": 1437, "label": "EVAL-BACKTRACK" }, { "from": 1435, "to": 2014, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT905 -> s(0)" }, { "from": 1435, "to": 2015, "label": "EVAL-BACKTRACK" }, { "from": 1436, "to": 1442, "label": "GENERALIZATION\nT912 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT912 is ground" }, { "from": 1442, "to": 1443, "label": "CASE" }, { "from": 1443, "to": 1446, "label": "PARALLEL" }, { "from": 1443, "to": 1447, "label": "PARALLEL" }, { "from": 1446, "to": 1455, "label": "EVAL with clause\nlog2(s(s(X1627)), X1628, X1629, X1630) :- log2(X1627, s(X1628), X1629, X1630).\nand substitutionX1627 -> T928,\nT906 -> s(s(T928)),\nX1628 -> s(0),\nT912 -> T929,\nX1629 -> s(T929),\nT907 -> T930,\nX1630 -> T930" }, { "from": 1446, "to": 1456, "label": "EVAL-BACKTRACK" }, { "from": 1447, "to": 1994, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1455, "to": 1457, "label": "CASE" }, { "from": 1457, "to": 1460, "label": "PARALLEL" }, { "from": 1457, "to": 1461, "label": "PARALLEL" }, { "from": 1460, "to": 1463, "label": "EVAL with clause\nlog2(s(s(X1651)), X1652, X1653, X1654) :- log2(X1651, s(X1652), X1653, X1654).\nand substitutionX1651 -> T946,\nT928 -> s(s(T946)),\nX1652 -> s(s(0)),\nT929 -> T947,\nX1653 -> s(T947),\nT930 -> T948,\nX1654 -> T948" }, { "from": 1460, "to": 1464, "label": "EVAL-BACKTRACK" }, { "from": 1461, "to": 1936, "label": "PARALLEL" }, { "from": 1461, "to": 1937, "label": "PARALLEL" }, { "from": 1463, "to": 1467, "label": "CASE" }, { "from": 1467, "to": 1470, "label": "PARALLEL" }, { "from": 1467, "to": 1471, "label": "PARALLEL" }, { "from": 1470, "to": 1473, "label": "EVAL with clause\nlog2(s(s(X1675)), X1676, X1677, X1678) :- log2(X1675, s(X1676), X1677, X1678).\nand substitutionX1675 -> T964,\nT946 -> s(s(T964)),\nX1676 -> s(s(s(0))),\nT947 -> T965,\nX1677 -> s(T965),\nT948 -> T966,\nX1678 -> T966" }, { "from": 1470, "to": 1474, "label": "EVAL-BACKTRACK" }, { "from": 1471, "to": 1884, "label": "PARALLEL" }, { "from": 1471, "to": 1885, "label": "PARALLEL" }, { "from": 1473, "to": 1477, "label": "CASE" }, { "from": 1477, "to": 1487, "label": "PARALLEL" }, { "from": 1477, "to": 1488, "label": "PARALLEL" }, { "from": 1487, "to": 1497, "label": "EVAL with clause\nlog2(s(s(X1699)), X1700, X1701, X1702) :- log2(X1699, s(X1700), X1701, X1702).\nand substitutionX1699 -> T982,\nT964 -> s(s(T982)),\nX1700 -> s(s(s(s(0)))),\nT965 -> T983,\nX1701 -> s(T983),\nT966 -> T984,\nX1702 -> T984" }, { "from": 1487, "to": 1498, "label": "EVAL-BACKTRACK" }, { "from": 1488, "to": 1819, "label": "PARALLEL" }, { "from": 1488, "to": 1820, "label": "PARALLEL" }, { "from": 1497, "to": 1499, "label": "CASE" }, { "from": 1499, "to": 1502, "label": "PARALLEL" }, { "from": 1499, "to": 1503, "label": "PARALLEL" }, { "from": 1502, "to": 1523, "label": "EVAL with clause\nlog2(s(s(X1723)), X1724, X1725, X1726) :- log2(X1723, s(X1724), X1725, X1726).\nand substitutionX1723 -> T1000,\nT982 -> s(s(T1000)),\nX1724 -> s(s(s(s(s(0))))),\nT983 -> T1001,\nX1725 -> s(T1001),\nT984 -> T1002,\nX1726 -> T1002" }, { "from": 1502, "to": 1524, "label": "EVAL-BACKTRACK" }, { "from": 1503, "to": 1756, "label": "PARALLEL" }, { "from": 1503, "to": 1757, "label": "PARALLEL" }, { "from": 1523, "to": 1529, "label": "CASE" }, { "from": 1529, "to": 1538, "label": "PARALLEL" }, { "from": 1529, "to": 1539, "label": "PARALLEL" }, { "from": 1538, "to": 1544, "label": "EVAL with clause\nlog2(s(s(X1747)), X1748, X1749, X1750) :- log2(X1747, s(X1748), X1749, X1750).\nand substitutionX1747 -> T1018,\nT1000 -> s(s(T1018)),\nX1748 -> s(s(s(s(s(s(0)))))),\nT1001 -> T1019,\nX1749 -> s(T1019),\nT1002 -> T1020,\nX1750 -> T1020" }, { "from": 1538, "to": 1547, "label": "EVAL-BACKTRACK" }, { "from": 1539, "to": 1710, "label": "PARALLEL" }, { "from": 1539, "to": 1711, "label": "PARALLEL" }, { "from": 1544, "to": 1565, "label": "CASE" }, { "from": 1565, "to": 1592, "label": "PARALLEL" }, { "from": 1565, "to": 1593, "label": "PARALLEL" }, { "from": 1592, "to": 1603, "label": "EVAL with clause\nlog2(s(s(X1771)), X1772, X1773, X1774) :- log2(X1771, s(X1772), X1773, X1774).\nand substitutionX1771 -> T1036,\nT1018 -> s(s(T1036)),\nX1772 -> s(s(s(s(s(s(s(0))))))),\nT1019 -> T1037,\nX1773 -> s(T1037),\nT1020 -> T1038,\nX1774 -> T1038" }, { "from": 1592, "to": 1606, "label": "EVAL-BACKTRACK" }, { "from": 1593, "to": 1673, "label": "PARALLEL" }, { "from": 1593, "to": 1674, "label": "PARALLEL" }, { "from": 1603, "to": 1608, "label": "GENERALIZATION\nT1042 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT1042 is ground" }, { "from": 1608, "to": 1626, "label": "CASE" }, { "from": 1626, "to": 1629, "label": "PARALLEL" }, { "from": 1626, "to": 1630, "label": "PARALLEL" }, { "from": 1629, "to": 1636, "label": "EVAL with clause\nlog2(s(s(X1799)), X1800, X1801, X1802) :- log2(X1799, s(X1800), X1801, X1802).\nand substitutionX1799 -> T1063,\nT1036 -> s(s(T1063)),\nT1042 -> T1064,\nX1800 -> s(T1064),\nT1037 -> T1065,\nX1801 -> s(T1065),\nT1038 -> T1066,\nX1802 -> T1066" }, { "from": 1629, "to": 1637, "label": "EVAL-BACKTRACK" }, { "from": 1630, "to": 1640, "label": "PARALLEL" }, { "from": 1630, "to": 1641, "label": "PARALLEL" }, { "from": 1636, "to": 1608, "label": "INSTANCE with matching:\nT1036 -> T1063\nT1042 -> s(T1064)\nT1037 -> T1065\nT1038 -> T1066" }, { "from": 1640, "to": 1645, "label": "EVAL with clause\nlog2(X1823, s(s(X1824)), X1825, X1826) :- ','(small(X1823), log2(X1824, s(0), s(X1825), X1826)).\nand substitutionT1036 -> T1087,\nX1823 -> T1087,\nX1824 -> T1088,\nT1042 -> s(T1088),\nT1037 -> T1089,\nX1825 -> s(T1089),\nT1038 -> T1090,\nX1826 -> T1090" }, { "from": 1640, "to": 1646, "label": "EVAL-BACKTRACK" }, { "from": 1641, "to": 1654, "label": "EVAL with clause\nlog2(X1845, X1846, X1847, X1847) :- ','(small(X1845), small(X1846)).\nand substitutionT1036 -> T1106,\nX1845 -> T1106,\nT1042 -> T1107,\nX1846 -> s(T1107),\nT1037 -> T1108,\nX1847 -> s(T1108),\nT1038 -> s(T1108)" }, { "from": 1641, "to": 1655, "label": "EVAL-BACKTRACK" }, { "from": 1645, "to": 1647, "label": "CASE" }, { "from": 1647, "to": 1648, "label": "PARALLEL" }, { "from": 1647, "to": 1649, "label": "PARALLEL" }, { "from": 1648, "to": 1650, "label": "EVAL with clause\nsmall(0).\nand substitutionT1087 -> 0" }, { "from": 1648, "to": 1651, "label": "EVAL-BACKTRACK" }, { "from": 1649, "to": 1652, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1087 -> s(0)" }, { "from": 1649, "to": 1653, "label": "EVAL-BACKTRACK" }, { "from": 1650, "to": 1442, "label": "INSTANCE with matching:\nT906 -> T1088\nT912 -> s(T1089)\nT907 -> T1090" }, { "from": 1652, "to": 1442, "label": "INSTANCE with matching:\nT906 -> T1088\nT912 -> s(T1089)\nT907 -> T1090" }, { "from": 1654, "to": 1656, "label": "CASE" }, { "from": 1656, "to": 1657, "label": "PARALLEL" }, { "from": 1656, "to": 1658, "label": "PARALLEL" }, { "from": 1657, "to": 1659, "label": "EVAL with clause\nsmall(0).\nand substitutionT1106 -> 0" }, { "from": 1657, "to": 1660, "label": "EVAL-BACKTRACK" }, { "from": 1658, "to": 1666, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1106 -> s(0)" }, { "from": 1658, "to": 1667, "label": "EVAL-BACKTRACK" }, { "from": 1659, "to": 1661, "label": "CASE" }, { "from": 1661, "to": 1662, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1662, "to": 1663, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1107 -> 0" }, { "from": 1662, "to": 1664, "label": "EVAL-BACKTRACK" }, { "from": 1663, "to": 1665, "label": "SUCCESS" }, { "from": 1666, "to": 1668, "label": "CASE" }, { "from": 1668, "to": 1669, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1669, "to": 1670, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1107 -> 0" }, { "from": 1669, "to": 1671, "label": "EVAL-BACKTRACK" }, { "from": 1670, "to": 1672, "label": "SUCCESS" }, { "from": 1673, "to": 1677, "label": "ONLY EVAL with clause\nlog2(X1872, s(s(X1873)), X1874, X1875) :- ','(small(X1872), log2(X1873, s(0), s(X1874), X1875)).\nand substitutionT1018 -> T1125,\nX1872 -> T1125,\nX1873 -> s(s(s(s(s(0))))),\nT1019 -> T1126,\nX1874 -> s(T1126),\nT1020 -> T1127,\nX1875 -> T1127" }, { "from": 1674, "to": 1693, "label": "EVAL with clause\nlog2(X1894, X1895, X1896, X1896) :- ','(small(X1894), small(X1895)).\nand substitutionT1018 -> T1138,\nX1894 -> T1138,\nX1895 -> s(s(s(s(s(s(s(0))))))),\nT1019 -> T1139,\nX1896 -> s(T1139),\nT1020 -> s(T1139)" }, { "from": 1674, "to": 1694, "label": "EVAL-BACKTRACK" }, { "from": 1677, "to": 1682, "label": "CASE" }, { "from": 1682, "to": 1683, "label": "PARALLEL" }, { "from": 1682, "to": 1684, "label": "PARALLEL" }, { "from": 1683, "to": 1685, "label": "EVAL with clause\nsmall(0).\nand substitutionT1125 -> 0" }, { "from": 1683, "to": 1686, "label": "EVAL-BACKTRACK" }, { "from": 1684, "to": 1687, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1125 -> s(0)" }, { "from": 1684, "to": 1688, "label": "EVAL-BACKTRACK" }, { "from": 1685, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(s(0)))))\nT912 -> s(T1126)\nT907 -> T1127" }, { "from": 1687, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(s(0)))))\nT912 -> s(T1126)\nT907 -> T1127" }, { "from": 1693, "to": 1695, "label": "CASE" }, { "from": 1695, "to": 1696, "label": "PARALLEL" }, { "from": 1695, "to": 1697, "label": "PARALLEL" }, { "from": 1696, "to": 1698, "label": "EVAL with clause\nsmall(0).\nand substitutionT1138 -> 0" }, { "from": 1696, "to": 1699, "label": "EVAL-BACKTRACK" }, { "from": 1697, "to": 1703, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1138 -> s(0)" }, { "from": 1697, "to": 1704, "label": "EVAL-BACKTRACK" }, { "from": 1698, "to": 1700, "label": "CASE" }, { "from": 1700, "to": 1701, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1701, "to": 1702, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1703, "to": 1705, "label": "CASE" }, { "from": 1705, "to": 1706, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1706, "to": 1707, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1710, "to": 1716, "label": "ONLY EVAL with clause\nlog2(X1921, s(s(X1922)), X1923, X1924) :- ','(small(X1921), log2(X1922, s(0), s(X1923), X1924)).\nand substitutionT1000 -> T1156,\nX1921 -> T1156,\nX1922 -> s(s(s(s(0)))),\nT1001 -> T1157,\nX1923 -> s(T1157),\nT1002 -> T1158,\nX1924 -> T1158" }, { "from": 1711, "to": 1733, "label": "EVAL with clause\nlog2(X1943, X1944, X1945, X1945) :- ','(small(X1943), small(X1944)).\nand substitutionT1000 -> T1169,\nX1943 -> T1169,\nX1944 -> s(s(s(s(s(s(0)))))),\nT1001 -> T1170,\nX1945 -> s(T1170),\nT1002 -> s(T1170)" }, { "from": 1711, "to": 1734, "label": "EVAL-BACKTRACK" }, { "from": 1716, "to": 1717, "label": "CASE" }, { "from": 1717, "to": 1718, "label": "PARALLEL" }, { "from": 1717, "to": 1719, "label": "PARALLEL" }, { "from": 1718, "to": 1720, "label": "EVAL with clause\nsmall(0).\nand substitutionT1156 -> 0" }, { "from": 1718, "to": 1721, "label": "EVAL-BACKTRACK" }, { "from": 1719, "to": 1722, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1156 -> s(0)" }, { "from": 1719, "to": 1723, "label": "EVAL-BACKTRACK" }, { "from": 1720, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(0))))\nT912 -> s(T1157)\nT907 -> T1158" }, { "from": 1722, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(0))))\nT912 -> s(T1157)\nT907 -> T1158" }, { "from": 1733, "to": 1735, "label": "CASE" }, { "from": 1735, "to": 1736, "label": "PARALLEL" }, { "from": 1735, "to": 1737, "label": "PARALLEL" }, { "from": 1736, "to": 1738, "label": "EVAL with clause\nsmall(0).\nand substitutionT1169 -> 0" }, { "from": 1736, "to": 1739, "label": "EVAL-BACKTRACK" }, { "from": 1737, "to": 1743, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1169 -> s(0)" }, { "from": 1737, "to": 1744, "label": "EVAL-BACKTRACK" }, { "from": 1738, "to": 1740, "label": "CASE" }, { "from": 1740, "to": 1741, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1741, "to": 1742, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1743, "to": 1745, "label": "CASE" }, { "from": 1745, "to": 1746, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1746, "to": 1747, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1756, "to": 1773, "label": "ONLY EVAL with clause\nlog2(X1970, s(s(X1971)), X1972, X1973) :- ','(small(X1970), log2(X1971, s(0), s(X1972), X1973)).\nand substitutionT982 -> T1187,\nX1970 -> T1187,\nX1971 -> s(s(s(0))),\nT983 -> T1188,\nX1972 -> s(T1188),\nT984 -> T1189,\nX1973 -> T1189" }, { "from": 1757, "to": 1789, "label": "EVAL with clause\nlog2(X1992, X1993, X1994, X1994) :- ','(small(X1992), small(X1993)).\nand substitutionT982 -> T1200,\nX1992 -> T1200,\nX1993 -> s(s(s(s(s(0))))),\nT983 -> T1201,\nX1994 -> s(T1201),\nT984 -> s(T1201)" }, { "from": 1757, "to": 1790, "label": "EVAL-BACKTRACK" }, { "from": 1773, "to": 1774, "label": "CASE" }, { "from": 1774, "to": 1775, "label": "PARALLEL" }, { "from": 1774, "to": 1776, "label": "PARALLEL" }, { "from": 1775, "to": 1777, "label": "EVAL with clause\nsmall(0).\nand substitutionT1187 -> 0" }, { "from": 1775, "to": 1778, "label": "EVAL-BACKTRACK" }, { "from": 1776, "to": 1779, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1187 -> s(0)" }, { "from": 1776, "to": 1780, "label": "EVAL-BACKTRACK" }, { "from": 1777, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(0)))\nT912 -> s(T1188)\nT907 -> T1189" }, { "from": 1779, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(0)))\nT912 -> s(T1188)\nT907 -> T1189" }, { "from": 1789, "to": 1791, "label": "CASE" }, { "from": 1791, "to": 1792, "label": "PARALLEL" }, { "from": 1791, "to": 1793, "label": "PARALLEL" }, { "from": 1792, "to": 1794, "label": "EVAL with clause\nsmall(0).\nand substitutionT1200 -> 0" }, { "from": 1792, "to": 1795, "label": "EVAL-BACKTRACK" }, { "from": 1793, "to": 1799, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1200 -> s(0)" }, { "from": 1793, "to": 1800, "label": "EVAL-BACKTRACK" }, { "from": 1794, "to": 1796, "label": "CASE" }, { "from": 1796, "to": 1797, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1797, "to": 1798, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1799, "to": 1801, "label": "CASE" }, { "from": 1801, "to": 1802, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1802, "to": 1803, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1819, "to": 1825, "label": "ONLY EVAL with clause\nlog2(X2019, s(s(X2020)), X2021, X2022) :- ','(small(X2019), log2(X2020, s(0), s(X2021), X2022)).\nand substitutionT964 -> T1218,\nX2019 -> T1218,\nX2020 -> s(s(0)),\nT965 -> T1219,\nX2021 -> s(T1219),\nT966 -> T1220,\nX2022 -> T1220" }, { "from": 1820, "to": 1854, "label": "EVAL with clause\nlog2(X2041, X2042, X2043, X2043) :- ','(small(X2041), small(X2042)).\nand substitutionT964 -> T1231,\nX2041 -> T1231,\nX2042 -> s(s(s(s(0)))),\nT965 -> T1232,\nX2043 -> s(T1232),\nT966 -> s(T1232)" }, { "from": 1820, "to": 1856, "label": "EVAL-BACKTRACK" }, { "from": 1825, "to": 1827, "label": "CASE" }, { "from": 1827, "to": 1828, "label": "PARALLEL" }, { "from": 1827, "to": 1829, "label": "PARALLEL" }, { "from": 1828, "to": 1830, "label": "EVAL with clause\nsmall(0).\nand substitutionT1218 -> 0" }, { "from": 1828, "to": 1831, "label": "EVAL-BACKTRACK" }, { "from": 1829, "to": 1850, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1218 -> s(0)" }, { "from": 1829, "to": 1851, "label": "EVAL-BACKTRACK" }, { "from": 1830, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(0))\nT912 -> s(T1219)\nT907 -> T1220" }, { "from": 1850, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(0))\nT912 -> s(T1219)\nT907 -> T1220" }, { "from": 1854, "to": 1858, "label": "CASE" }, { "from": 1858, "to": 1860, "label": "PARALLEL" }, { "from": 1858, "to": 1862, "label": "PARALLEL" }, { "from": 1860, "to": 1865, "label": "EVAL with clause\nsmall(0).\nand substitutionT1231 -> 0" }, { "from": 1860, "to": 1867, "label": "EVAL-BACKTRACK" }, { "from": 1862, "to": 1876, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1231 -> s(0)" }, { "from": 1862, "to": 1877, "label": "EVAL-BACKTRACK" }, { "from": 1865, "to": 1869, "label": "CASE" }, { "from": 1869, "to": 1872, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1872, "to": 1873, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1876, "to": 1881, "label": "CASE" }, { "from": 1881, "to": 1882, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1882, "to": 1883, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1884, "to": 1888, "label": "ONLY EVAL with clause\nlog2(X2068, s(s(X2069)), X2070, X2071) :- ','(small(X2068), log2(X2069, s(0), s(X2070), X2071)).\nand substitutionT946 -> T1245,\nX2068 -> T1245,\nX2069 -> s(0),\nT947 -> T1246,\nX2070 -> s(T1246),\nT948 -> T1247,\nX2071 -> T1247" }, { "from": 1885, "to": 1906, "label": "EVAL with clause\nlog2(X2090, X2091, X2092, X2092) :- ','(small(X2090), small(X2091)).\nand substitutionT946 -> T1252,\nX2090 -> T1252,\nX2091 -> s(s(s(0))),\nT947 -> T1253,\nX2092 -> s(T1253),\nT948 -> s(T1253)" }, { "from": 1885, "to": 1907, "label": "EVAL-BACKTRACK" }, { "from": 1888, "to": 1895, "label": "CASE" }, { "from": 1895, "to": 1896, "label": "PARALLEL" }, { "from": 1895, "to": 1897, "label": "PARALLEL" }, { "from": 1896, "to": 1898, "label": "EVAL with clause\nsmall(0).\nand substitutionT1245 -> 0" }, { "from": 1896, "to": 1899, "label": "EVAL-BACKTRACK" }, { "from": 1897, "to": 1902, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1245 -> s(0)" }, { "from": 1897, "to": 1903, "label": "EVAL-BACKTRACK" }, { "from": 1898, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(0)\nT912 -> s(T1246)\nT907 -> T1247" }, { "from": 1902, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(0)\nT912 -> s(T1246)\nT907 -> T1247" }, { "from": 1906, "to": 1908, "label": "CASE" }, { "from": 1908, "to": 1909, "label": "PARALLEL" }, { "from": 1908, "to": 1910, "label": "PARALLEL" }, { "from": 1909, "to": 1911, "label": "EVAL with clause\nsmall(0).\nand substitutionT1252 -> 0" }, { "from": 1909, "to": 1912, "label": "EVAL-BACKTRACK" }, { "from": 1910, "to": 1918, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1252 -> s(0)" }, { "from": 1910, "to": 1919, "label": "EVAL-BACKTRACK" }, { "from": 1911, "to": 1913, "label": "CASE" }, { "from": 1913, "to": 1914, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1914, "to": 1916, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1918, "to": 1922, "label": "CASE" }, { "from": 1922, "to": 1924, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1924, "to": 1925, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1936, "to": 1940, "label": "ONLY EVAL with clause\nlog2(X2117, s(s(X2118)), X2119, X2120) :- ','(small(X2117), log2(X2118, s(0), s(X2119), X2120)).\nand substitutionT928 -> T1266,\nX2117 -> T1266,\nX2118 -> 0,\nT929 -> T1267,\nX2119 -> s(T1267),\nT930 -> T1268,\nX2120 -> T1268" }, { "from": 1937, "to": 1964, "label": "EVAL with clause\nlog2(X2139, X2140, X2141, X2141) :- ','(small(X2139), small(X2140)).\nand substitutionT928 -> T1273,\nX2139 -> T1273,\nX2140 -> s(s(0)),\nT929 -> T1274,\nX2141 -> s(T1274),\nT930 -> s(T1274)" }, { "from": 1937, "to": 1965, "label": "EVAL-BACKTRACK" }, { "from": 1940, "to": 1942, "label": "CASE" }, { "from": 1942, "to": 1943, "label": "PARALLEL" }, { "from": 1942, "to": 1944, "label": "PARALLEL" }, { "from": 1943, "to": 1945, "label": "EVAL with clause\nsmall(0).\nand substitutionT1266 -> 0" }, { "from": 1943, "to": 1946, "label": "EVAL-BACKTRACK" }, { "from": 1944, "to": 1952, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1266 -> s(0)" }, { "from": 1944, "to": 1953, "label": "EVAL-BACKTRACK" }, { "from": 1945, "to": 1442, "label": "INSTANCE with matching:\nT906 -> 0\nT912 -> s(T1267)\nT907 -> T1268" }, { "from": 1952, "to": 1442, "label": "INSTANCE with matching:\nT906 -> 0\nT912 -> s(T1267)\nT907 -> T1268" }, { "from": 1964, "to": 1968, "label": "CASE" }, { "from": 1968, "to": 1969, "label": "PARALLEL" }, { "from": 1968, "to": 1971, "label": "PARALLEL" }, { "from": 1969, "to": 1974, "label": "EVAL with clause\nsmall(0).\nand substitutionT1273 -> 0" }, { "from": 1969, "to": 1975, "label": "EVAL-BACKTRACK" }, { "from": 1971, "to": 1984, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1273 -> s(0)" }, { "from": 1971, "to": 1985, "label": "EVAL-BACKTRACK" }, { "from": 1974, "to": 1978, "label": "CASE" }, { "from": 1978, "to": 1979, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1979, "to": 1980, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1984, "to": 1988, "label": "CASE" }, { "from": 1988, "to": 1989, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1989, "to": 1990, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1994, "to": 1997, "label": "EVAL with clause\nlog2(X2152, X2153, X2154, X2154) :- ','(small(X2152), small(X2153)).\nand substitutionT906 -> T1280,\nX2152 -> T1280,\nX2153 -> s(0),\nT912 -> T1281,\nX2154 -> s(T1281),\nT907 -> s(T1281)" }, { "from": 1994, "to": 1998, "label": "EVAL-BACKTRACK" }, { "from": 1997, "to": 1999, "label": "CASE" }, { "from": 1999, "to": 2000, "label": "PARALLEL" }, { "from": 1999, "to": 2001, "label": "PARALLEL" }, { "from": 2000, "to": 2002, "label": "EVAL with clause\nsmall(0).\nand substitutionT1280 -> 0" }, { "from": 2000, "to": 2003, "label": "EVAL-BACKTRACK" }, { "from": 2001, "to": 2008, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1280 -> s(0)" }, { "from": 2001, "to": 2009, "label": "EVAL-BACKTRACK" }, { "from": 2002, "to": 2004, "label": "CASE" }, { "from": 2004, "to": 2005, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2005, "to": 2006, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2006, "to": 2007, "label": "SUCCESS" }, { "from": 2008, "to": 2010, "label": "CASE" }, { "from": 2010, "to": 2011, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2011, "to": 2012, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2012, "to": 2013, "label": "SUCCESS" }, { "from": 2014, "to": 1442, "label": "INSTANCE with matching:\nT912 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2022, "to": 2024, "label": "CASE" }, { "from": 2024, "to": 2025, "label": "PARALLEL" }, { "from": 2024, "to": 2026, "label": "PARALLEL" }, { "from": 2025, "to": 2027, "label": "EVAL with clause\nsmall(0).\nand substitutionT1288 -> 0" }, { "from": 2025, "to": 2028, "label": "EVAL-BACKTRACK" }, { "from": 2026, "to": 2034, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1288 -> s(0)" }, { "from": 2026, "to": 2036, "label": "EVAL-BACKTRACK" }, { "from": 2027, "to": 2029, "label": "CASE" }, { "from": 2029, "to": 2030, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2030, "to": 2031, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1289 -> 0" }, { "from": 2030, "to": 2032, "label": "EVAL-BACKTRACK" }, { "from": 2031, "to": 2033, "label": "SUCCESS" }, { "from": 2034, "to": 2038, "label": "CASE" }, { "from": 2038, "to": 2039, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2039, "to": 2040, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1289 -> 0" }, { "from": 2039, "to": 2041, "label": "EVAL-BACKTRACK" }, { "from": 2040, "to": 2042, "label": "SUCCESS" }, { "from": 2058, "to": 2077, "label": "ONLY EVAL with clause\nlog2(X2192, s(s(X2193)), X2194, X2195) :- ','(small(X2192), log2(X2193, s(0), s(X2194), X2195)).\nand substitutionT855 -> T1300,\nX2192 -> T1300,\nX2193 -> s(s(s(s(s(0))))),\nX2194 -> s(s(s(s(s(s(s(0))))))),\nT856 -> T1301,\nX2195 -> T1301" }, { "from": 2059, "to": 2095, "label": "EVAL with clause\nlog2(X2214, X2215, X2216, X2216) :- ','(small(X2214), small(X2215)).\nand substitutionT855 -> T1307,\nX2214 -> T1307,\nX2215 -> s(s(s(s(s(s(s(0))))))),\nX2216 -> s(s(s(s(s(s(s(0))))))),\nT856 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2059, "to": 2096, "label": "EVAL-BACKTRACK" }, { "from": 2077, "to": 2078, "label": "CASE" }, { "from": 2078, "to": 2079, "label": "PARALLEL" }, { "from": 2078, "to": 2080, "label": "PARALLEL" }, { "from": 2079, "to": 2081, "label": "EVAL with clause\nsmall(0).\nand substitutionT1300 -> 0" }, { "from": 2079, "to": 2082, "label": "EVAL-BACKTRACK" }, { "from": 2080, "to": 2085, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1300 -> s(0)" }, { "from": 2080, "to": 2086, "label": "EVAL-BACKTRACK" }, { "from": 2081, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(s(0)))))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1301" }, { "from": 2085, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(s(0)))))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1301" }, { "from": 2095, "to": 2097, "label": "CASE" }, { "from": 2097, "to": 2098, "label": "PARALLEL" }, { "from": 2097, "to": 2099, "label": "PARALLEL" }, { "from": 2098, "to": 2100, "label": "EVAL with clause\nsmall(0).\nand substitutionT1307 -> 0" }, { "from": 2098, "to": 2101, "label": "EVAL-BACKTRACK" }, { "from": 2099, "to": 2105, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1307 -> s(0)" }, { "from": 2099, "to": 2106, "label": "EVAL-BACKTRACK" }, { "from": 2100, "to": 2102, "label": "CASE" }, { "from": 2102, "to": 2103, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2103, "to": 2104, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2105, "to": 2107, "label": "CASE" }, { "from": 2107, "to": 2108, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2108, "to": 2109, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2125, "to": 2174, "label": "ONLY EVAL with clause\nlog2(X2241, s(s(X2242)), X2243, X2244) :- ','(small(X2241), log2(X2242, s(0), s(X2243), X2244)).\nand substitutionT843 -> T1318,\nX2241 -> T1318,\nX2242 -> s(s(s(s(0)))),\nX2243 -> s(s(s(s(s(s(s(0))))))),\nT844 -> T1319,\nX2244 -> T1319" }, { "from": 2126, "to": 2211, "label": "EVAL with clause\nlog2(X2263, X2264, X2265, X2265) :- ','(small(X2263), small(X2264)).\nand substitutionT843 -> T1325,\nX2263 -> T1325,\nX2264 -> s(s(s(s(s(s(0)))))),\nX2265 -> s(s(s(s(s(s(s(0))))))),\nT844 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2126, "to": 2212, "label": "EVAL-BACKTRACK" }, { "from": 2174, "to": 2183, "label": "CASE" }, { "from": 2183, "to": 2184, "label": "PARALLEL" }, { "from": 2183, "to": 2185, "label": "PARALLEL" }, { "from": 2184, "to": 2186, "label": "EVAL with clause\nsmall(0).\nand substitutionT1318 -> 0" }, { "from": 2184, "to": 2187, "label": "EVAL-BACKTRACK" }, { "from": 2185, "to": 2192, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1318 -> s(0)" }, { "from": 2185, "to": 2193, "label": "EVAL-BACKTRACK" }, { "from": 2186, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(0))))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1319" }, { "from": 2192, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(s(0))))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1319" }, { "from": 2211, "to": 2213, "label": "CASE" }, { "from": 2213, "to": 2214, "label": "PARALLEL" }, { "from": 2213, "to": 2215, "label": "PARALLEL" }, { "from": 2214, "to": 2216, "label": "EVAL with clause\nsmall(0).\nand substitutionT1325 -> 0" }, { "from": 2214, "to": 2217, "label": "EVAL-BACKTRACK" }, { "from": 2215, "to": 2221, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1325 -> s(0)" }, { "from": 2215, "to": 2222, "label": "EVAL-BACKTRACK" }, { "from": 2216, "to": 2218, "label": "CASE" }, { "from": 2218, "to": 2219, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2219, "to": 2220, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2221, "to": 2223, "label": "CASE" }, { "from": 2223, "to": 2224, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2224, "to": 2225, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2243, "to": 2253, "label": "ONLY EVAL with clause\nlog2(X2290, s(s(X2291)), X2292, X2293) :- ','(small(X2290), log2(X2291, s(0), s(X2292), X2293)).\nand substitutionT831 -> T1336,\nX2290 -> T1336,\nX2291 -> s(s(s(0))),\nX2292 -> s(s(s(s(s(s(s(0))))))),\nT832 -> T1337,\nX2293 -> T1337" }, { "from": 2244, "to": 2296, "label": "EVAL with clause\nlog2(X2312, X2313, X2314, X2314) :- ','(small(X2312), small(X2313)).\nand substitutionT831 -> T1343,\nX2312 -> T1343,\nX2313 -> s(s(s(s(s(0))))),\nX2314 -> s(s(s(s(s(s(s(0))))))),\nT832 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2244, "to": 2297, "label": "EVAL-BACKTRACK" }, { "from": 2253, "to": 2254, "label": "CASE" }, { "from": 2254, "to": 2256, "label": "PARALLEL" }, { "from": 2254, "to": 2257, "label": "PARALLEL" }, { "from": 2256, "to": 2258, "label": "EVAL with clause\nsmall(0).\nand substitutionT1336 -> 0" }, { "from": 2256, "to": 2259, "label": "EVAL-BACKTRACK" }, { "from": 2257, "to": 2267, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1336 -> s(0)" }, { "from": 2257, "to": 2268, "label": "EVAL-BACKTRACK" }, { "from": 2258, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(0)))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1337" }, { "from": 2267, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(s(0)))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1337" }, { "from": 2296, "to": 2298, "label": "CASE" }, { "from": 2298, "to": 2299, "label": "PARALLEL" }, { "from": 2298, "to": 2300, "label": "PARALLEL" }, { "from": 2299, "to": 2301, "label": "EVAL with clause\nsmall(0).\nand substitutionT1343 -> 0" }, { "from": 2299, "to": 2302, "label": "EVAL-BACKTRACK" }, { "from": 2300, "to": 2306, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1343 -> s(0)" }, { "from": 2300, "to": 2307, "label": "EVAL-BACKTRACK" }, { "from": 2301, "to": 2303, "label": "CASE" }, { "from": 2303, "to": 2304, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2304, "to": 2305, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2306, "to": 2308, "label": "CASE" }, { "from": 2308, "to": 2309, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2309, "to": 2310, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2311, "to": 2335, "label": "ONLY EVAL with clause\nlog2(X2339, s(s(X2340)), X2341, X2342) :- ','(small(X2339), log2(X2340, s(0), s(X2341), X2342)).\nand substitutionT819 -> T1354,\nX2339 -> T1354,\nX2340 -> s(s(0)),\nX2341 -> s(s(s(s(s(s(s(0))))))),\nT820 -> T1355,\nX2342 -> T1355" }, { "from": 2312, "to": 2377, "label": "EVAL with clause\nlog2(X2361, X2362, X2363, X2363) :- ','(small(X2361), small(X2362)).\nand substitutionT819 -> T1361,\nX2361 -> T1361,\nX2362 -> s(s(s(s(0)))),\nX2363 -> s(s(s(s(s(s(s(0))))))),\nT820 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2312, "to": 2378, "label": "EVAL-BACKTRACK" }, { "from": 2335, "to": 2343, "label": "CASE" }, { "from": 2343, "to": 2346, "label": "PARALLEL" }, { "from": 2343, "to": 2347, "label": "PARALLEL" }, { "from": 2346, "to": 2351, "label": "EVAL with clause\nsmall(0).\nand substitutionT1354 -> 0" }, { "from": 2346, "to": 2352, "label": "EVAL-BACKTRACK" }, { "from": 2347, "to": 2354, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1354 -> s(0)" }, { "from": 2347, "to": 2355, "label": "EVAL-BACKTRACK" }, { "from": 2351, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(0))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1355" }, { "from": 2354, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(s(0))\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1355" }, { "from": 2377, "to": 2379, "label": "CASE" }, { "from": 2379, "to": 2380, "label": "PARALLEL" }, { "from": 2379, "to": 2381, "label": "PARALLEL" }, { "from": 2380, "to": 2382, "label": "EVAL with clause\nsmall(0).\nand substitutionT1361 -> 0" }, { "from": 2380, "to": 2383, "label": "EVAL-BACKTRACK" }, { "from": 2381, "to": 2387, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1361 -> s(0)" }, { "from": 2381, "to": 2388, "label": "EVAL-BACKTRACK" }, { "from": 2382, "to": 2384, "label": "CASE" }, { "from": 2384, "to": 2385, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2385, "to": 2386, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2387, "to": 2389, "label": "CASE" }, { "from": 2389, "to": 2390, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2390, "to": 2391, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2417, "to": 2423, "label": "ONLY EVAL with clause\nlog2(X2388, s(s(X2389)), X2390, X2391) :- ','(small(X2388), log2(X2389, s(0), s(X2390), X2391)).\nand substitutionT807 -> T1370,\nX2388 -> T1370,\nX2389 -> s(0),\nX2390 -> s(s(s(s(s(s(s(0))))))),\nT808 -> T1371,\nX2391 -> T1371" }, { "from": 2418, "to": 2448, "label": "EVAL with clause\nlog2(X2410, X2411, X2412, X2412) :- ','(small(X2410), small(X2411)).\nand substitutionT807 -> T1374,\nX2410 -> T1374,\nX2411 -> s(s(s(0))),\nX2412 -> s(s(s(s(s(s(s(0))))))),\nT808 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2418, "to": 2449, "label": "EVAL-BACKTRACK" }, { "from": 2423, "to": 2439, "label": "CASE" }, { "from": 2439, "to": 2440, "label": "PARALLEL" }, { "from": 2439, "to": 2441, "label": "PARALLEL" }, { "from": 2440, "to": 2442, "label": "EVAL with clause\nsmall(0).\nand substitutionT1370 -> 0" }, { "from": 2440, "to": 2443, "label": "EVAL-BACKTRACK" }, { "from": 2441, "to": 2444, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1370 -> s(0)" }, { "from": 2441, "to": 2445, "label": "EVAL-BACKTRACK" }, { "from": 2442, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(0)\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1371" }, { "from": 2444, "to": 1442, "label": "INSTANCE with matching:\nT906 -> s(0)\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1371" }, { "from": 2448, "to": 2450, "label": "CASE" }, { "from": 2450, "to": 2451, "label": "PARALLEL" }, { "from": 2450, "to": 2452, "label": "PARALLEL" }, { "from": 2451, "to": 2453, "label": "EVAL with clause\nsmall(0).\nand substitutionT1374 -> 0" }, { "from": 2451, "to": 2454, "label": "EVAL-BACKTRACK" }, { "from": 2452, "to": 2458, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1374 -> s(0)" }, { "from": 2452, "to": 2459, "label": "EVAL-BACKTRACK" }, { "from": 2453, "to": 2455, "label": "CASE" }, { "from": 2455, "to": 2456, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2456, "to": 2457, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2458, "to": 2460, "label": "CASE" }, { "from": 2460, "to": 2461, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2461, "to": 2462, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2481, "to": 2490, "label": "ONLY EVAL with clause\nlog2(X2437, s(s(X2438)), X2439, X2440) :- ','(small(X2437), log2(X2438, s(0), s(X2439), X2440)).\nand substitutionT795 -> T1383,\nX2437 -> T1383,\nX2438 -> 0,\nX2439 -> s(s(s(s(s(s(s(0))))))),\nT796 -> T1384,\nX2440 -> T1384" }, { "from": 2483, "to": 2531, "label": "EVAL with clause\nlog2(X2459, X2460, X2461, X2461) :- ','(small(X2459), small(X2460)).\nand substitutionT795 -> T1387,\nX2459 -> T1387,\nX2460 -> s(s(0)),\nX2461 -> s(s(s(s(s(s(s(0))))))),\nT796 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2483, "to": 2532, "label": "EVAL-BACKTRACK" }, { "from": 2490, "to": 2522, "label": "CASE" }, { "from": 2522, "to": 2523, "label": "PARALLEL" }, { "from": 2522, "to": 2524, "label": "PARALLEL" }, { "from": 2523, "to": 2525, "label": "EVAL with clause\nsmall(0).\nand substitutionT1383 -> 0" }, { "from": 2523, "to": 2526, "label": "EVAL-BACKTRACK" }, { "from": 2524, "to": 2527, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1383 -> s(0)" }, { "from": 2524, "to": 2528, "label": "EVAL-BACKTRACK" }, { "from": 2525, "to": 1442, "label": "INSTANCE with matching:\nT906 -> 0\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1384" }, { "from": 2527, "to": 1442, "label": "INSTANCE with matching:\nT906 -> 0\nT912 -> s(s(s(s(s(s(s(0)))))))\nT907 -> T1384" }, { "from": 2531, "to": 2533, "label": "CASE" }, { "from": 2533, "to": 2534, "label": "PARALLEL" }, { "from": 2533, "to": 2535, "label": "PARALLEL" }, { "from": 2534, "to": 2536, "label": "EVAL with clause\nsmall(0).\nand substitutionT1387 -> 0" }, { "from": 2534, "to": 2537, "label": "EVAL-BACKTRACK" }, { "from": 2535, "to": 2541, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1387 -> s(0)" }, { "from": 2535, "to": 2542, "label": "EVAL-BACKTRACK" }, { "from": 2536, "to": 2538, "label": "CASE" }, { "from": 2538, "to": 2539, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2539, "to": 2540, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2541, "to": 2543, "label": "CASE" }, { "from": 2543, "to": 2544, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2544, "to": 2545, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2569, "to": 2570, "label": "EVAL with clause\nlog2(X2472, X2473, X2474, X2474) :- ','(small(X2472), small(X2473)).\nand substitutionT781 -> T1391,\nX2472 -> T1391,\nX2473 -> s(0),\nX2474 -> s(s(s(s(s(s(s(0))))))),\nT782 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2569, "to": 2571, "label": "EVAL-BACKTRACK" }, { "from": 2570, "to": 2572, "label": "CASE" }, { "from": 2572, "to": 2575, "label": "PARALLEL" }, { "from": 2572, "to": 2576, "label": "PARALLEL" }, { "from": 2575, "to": 2577, "label": "EVAL with clause\nsmall(0).\nand substitutionT1391 -> 0" }, { "from": 2575, "to": 2578, "label": "EVAL-BACKTRACK" }, { "from": 2576, "to": 2585, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1391 -> s(0)" }, { "from": 2576, "to": 2586, "label": "EVAL-BACKTRACK" }, { "from": 2577, "to": 2581, "label": "CASE" }, { "from": 2581, "to": 2582, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2582, "to": 2583, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2583, "to": 2584, "label": "SUCCESS" }, { "from": 2585, "to": 2587, "label": "CASE" }, { "from": 2587, "to": 2588, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2588, "to": 2589, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2589, "to": 2590, "label": "SUCCESS" }, { "from": 2591, "to": 1286, "label": "INSTANCE" }, { "from": 2610, "to": 2612, "label": "CASE" }, { "from": 2612, "to": 2613, "label": "PARALLEL" }, { "from": 2612, "to": 2614, "label": "PARALLEL" }, { "from": 2613, "to": 2615, "label": "EVAL with clause\nsmall(0).\nand substitutionT1398 -> 0" }, { "from": 2613, "to": 2616, "label": "EVAL-BACKTRACK" }, { "from": 2614, "to": 2622, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1398 -> s(0)" }, { "from": 2614, "to": 2623, "label": "EVAL-BACKTRACK" }, { "from": 2615, "to": 2617, "label": "CASE" }, { "from": 2617, "to": 2618, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2618, "to": 2619, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1399 -> 0" }, { "from": 2618, "to": 2620, "label": "EVAL-BACKTRACK" }, { "from": 2619, "to": 2621, "label": "SUCCESS" }, { "from": 2622, "to": 2624, "label": "CASE" }, { "from": 2624, "to": 2625, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2625, "to": 2626, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1399 -> 0" }, { "from": 2625, "to": 2627, "label": "EVAL-BACKTRACK" }, { "from": 2626, "to": 2628, "label": "SUCCESS" }, { "from": 2645, "to": 2655, "label": "ONLY EVAL with clause\nlog2(X2512, s(s(X2513)), X2514, X2515) :- ','(small(X2512), log2(X2513, s(0), s(X2514), X2515)).\nand substitutionT730 -> T1410,\nX2512 -> T1410,\nX2513 -> s(s(s(s(s(0))))),\nX2514 -> s(s(s(s(s(s(0)))))),\nT731 -> T1411,\nX2515 -> T1411" }, { "from": 2646, "to": 2725, "label": "EVAL with clause\nlog2(X2534, X2535, X2536, X2536) :- ','(small(X2534), small(X2535)).\nand substitutionT730 -> T1417,\nX2534 -> T1417,\nX2535 -> s(s(s(s(s(s(s(0))))))),\nX2536 -> s(s(s(s(s(s(0)))))),\nT731 -> s(s(s(s(s(s(0))))))" }, { "from": 2646, "to": 2726, "label": "EVAL-BACKTRACK" }, { "from": 2655, "to": 2658, "label": "CASE" }, { "from": 2658, "to": 2659, "label": "PARALLEL" }, { "from": 2658, "to": 2660, "label": "PARALLEL" }, { "from": 2659, "to": 2661, "label": "EVAL with clause\nsmall(0).\nand substitutionT1410 -> 0" }, { "from": 2659, "to": 2662, "label": "EVAL-BACKTRACK" }, { "from": 2660, "to": 2696, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1410 -> s(0)" }, { "from": 2660, "to": 2697, "label": "EVAL-BACKTRACK" }, { "from": 2661, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(s(s(0)))))\nT782 -> T1411" }, { "from": 2696, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(s(s(0)))))\nT782 -> T1411" }, { "from": 2725, "to": 2727, "label": "CASE" }, { "from": 2727, "to": 2728, "label": "PARALLEL" }, { "from": 2727, "to": 2729, "label": "PARALLEL" }, { "from": 2728, "to": 2730, "label": "EVAL with clause\nsmall(0).\nand substitutionT1417 -> 0" }, { "from": 2728, "to": 2731, "label": "EVAL-BACKTRACK" }, { "from": 2729, "to": 2735, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1417 -> s(0)" }, { "from": 2729, "to": 2736, "label": "EVAL-BACKTRACK" }, { "from": 2730, "to": 2732, "label": "CASE" }, { "from": 2732, "to": 2733, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2733, "to": 2734, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2735, "to": 2737, "label": "CASE" }, { "from": 2737, "to": 2738, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2738, "to": 2739, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2790, "to": 2798, "label": "ONLY EVAL with clause\nlog2(X2561, s(s(X2562)), X2563, X2564) :- ','(small(X2561), log2(X2562, s(0), s(X2563), X2564)).\nand substitutionT718 -> T1428,\nX2561 -> T1428,\nX2562 -> s(s(s(s(0)))),\nX2563 -> s(s(s(s(s(s(0)))))),\nT719 -> T1429,\nX2564 -> T1429" }, { "from": 2791, "to": 2825, "label": "EVAL with clause\nlog2(X2583, X2584, X2585, X2585) :- ','(small(X2583), small(X2584)).\nand substitutionT718 -> T1435,\nX2583 -> T1435,\nX2584 -> s(s(s(s(s(s(0)))))),\nX2585 -> s(s(s(s(s(s(0)))))),\nT719 -> s(s(s(s(s(s(0))))))" }, { "from": 2791, "to": 2826, "label": "EVAL-BACKTRACK" }, { "from": 2798, "to": 2801, "label": "CASE" }, { "from": 2801, "to": 2802, "label": "PARALLEL" }, { "from": 2801, "to": 2803, "label": "PARALLEL" }, { "from": 2802, "to": 2804, "label": "EVAL with clause\nsmall(0).\nand substitutionT1428 -> 0" }, { "from": 2802, "to": 2805, "label": "EVAL-BACKTRACK" }, { "from": 2803, "to": 2806, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1428 -> s(0)" }, { "from": 2803, "to": 2807, "label": "EVAL-BACKTRACK" }, { "from": 2804, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(s(0))))\nT782 -> T1429" }, { "from": 2806, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(s(0))))\nT782 -> T1429" }, { "from": 2825, "to": 2827, "label": "CASE" }, { "from": 2827, "to": 2828, "label": "PARALLEL" }, { "from": 2827, "to": 2829, "label": "PARALLEL" }, { "from": 2828, "to": 2830, "label": "EVAL with clause\nsmall(0).\nand substitutionT1435 -> 0" }, { "from": 2828, "to": 2831, "label": "EVAL-BACKTRACK" }, { "from": 2829, "to": 2835, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1435 -> s(0)" }, { "from": 2829, "to": 2836, "label": "EVAL-BACKTRACK" }, { "from": 2830, "to": 2832, "label": "CASE" }, { "from": 2832, "to": 2833, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2833, "to": 2834, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2835, "to": 2837, "label": "CASE" }, { "from": 2837, "to": 2838, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2838, "to": 2839, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2840, "to": 2877, "label": "ONLY EVAL with clause\nlog2(X2610, s(s(X2611)), X2612, X2613) :- ','(small(X2610), log2(X2611, s(0), s(X2612), X2613)).\nand substitutionT706 -> T1446,\nX2610 -> T1446,\nX2611 -> s(s(s(0))),\nX2612 -> s(s(s(s(s(s(0)))))),\nT707 -> T1447,\nX2613 -> T1447" }, { "from": 2841, "to": 2920, "label": "EVAL with clause\nlog2(X2632, X2633, X2634, X2634) :- ','(small(X2632), small(X2633)).\nand substitutionT706 -> T1453,\nX2632 -> T1453,\nX2633 -> s(s(s(s(s(0))))),\nX2634 -> s(s(s(s(s(s(0)))))),\nT707 -> s(s(s(s(s(s(0))))))" }, { "from": 2841, "to": 2921, "label": "EVAL-BACKTRACK" }, { "from": 2877, "to": 2893, "label": "CASE" }, { "from": 2893, "to": 2894, "label": "PARALLEL" }, { "from": 2893, "to": 2895, "label": "PARALLEL" }, { "from": 2894, "to": 2909, "label": "EVAL with clause\nsmall(0).\nand substitutionT1446 -> 0" }, { "from": 2894, "to": 2913, "label": "EVAL-BACKTRACK" }, { "from": 2895, "to": 2915, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1446 -> s(0)" }, { "from": 2895, "to": 2916, "label": "EVAL-BACKTRACK" }, { "from": 2909, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(0)))\nT782 -> T1447" }, { "from": 2915, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(s(0)))\nT782 -> T1447" }, { "from": 2920, "to": 2922, "label": "CASE" }, { "from": 2922, "to": 2923, "label": "PARALLEL" }, { "from": 2922, "to": 2924, "label": "PARALLEL" }, { "from": 2923, "to": 2925, "label": "EVAL with clause\nsmall(0).\nand substitutionT1453 -> 0" }, { "from": 2923, "to": 2926, "label": "EVAL-BACKTRACK" }, { "from": 2924, "to": 2930, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1453 -> s(0)" }, { "from": 2924, "to": 2931, "label": "EVAL-BACKTRACK" }, { "from": 2925, "to": 2927, "label": "CASE" }, { "from": 2927, "to": 2928, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2928, "to": 2929, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2930, "to": 2932, "label": "CASE" }, { "from": 2932, "to": 2933, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2933, "to": 2934, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2935, "to": 2965, "label": "ONLY EVAL with clause\nlog2(X2659, s(s(X2660)), X2661, X2662) :- ','(small(X2659), log2(X2660, s(0), s(X2661), X2662)).\nand substitutionT694 -> T1464,\nX2659 -> T1464,\nX2660 -> s(s(0)),\nX2661 -> s(s(s(s(s(s(0)))))),\nT695 -> T1465,\nX2662 -> T1465" }, { "from": 2936, "to": 3015, "label": "EVAL with clause\nlog2(X2681, X2682, X2683, X2683) :- ','(small(X2681), small(X2682)).\nand substitutionT694 -> T1471,\nX2681 -> T1471,\nX2682 -> s(s(s(s(0)))),\nX2683 -> s(s(s(s(s(s(0)))))),\nT695 -> s(s(s(s(s(s(0))))))" }, { "from": 2936, "to": 3016, "label": "EVAL-BACKTRACK" }, { "from": 2965, "to": 2984, "label": "CASE" }, { "from": 2984, "to": 2985, "label": "PARALLEL" }, { "from": 2984, "to": 2986, "label": "PARALLEL" }, { "from": 2985, "to": 2987, "label": "EVAL with clause\nsmall(0).\nand substitutionT1464 -> 0" }, { "from": 2985, "to": 2988, "label": "EVAL-BACKTRACK" }, { "from": 2986, "to": 2991, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1464 -> s(0)" }, { "from": 2986, "to": 2992, "label": "EVAL-BACKTRACK" }, { "from": 2987, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(0))\nT782 -> T1465" }, { "from": 2991, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(s(0))\nT782 -> T1465" }, { "from": 3015, "to": 3017, "label": "CASE" }, { "from": 3017, "to": 3018, "label": "PARALLEL" }, { "from": 3017, "to": 3019, "label": "PARALLEL" }, { "from": 3018, "to": 3020, "label": "EVAL with clause\nsmall(0).\nand substitutionT1471 -> 0" }, { "from": 3018, "to": 3021, "label": "EVAL-BACKTRACK" }, { "from": 3019, "to": 3025, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1471 -> s(0)" }, { "from": 3019, "to": 3026, "label": "EVAL-BACKTRACK" }, { "from": 3020, "to": 3022, "label": "CASE" }, { "from": 3022, "to": 3023, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3023, "to": 3024, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3025, "to": 3027, "label": "CASE" }, { "from": 3027, "to": 3028, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3028, "to": 3029, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3036, "to": 3089, "label": "ONLY EVAL with clause\nlog2(X2708, s(s(X2709)), X2710, X2711) :- ','(small(X2708), log2(X2709, s(0), s(X2710), X2711)).\nand substitutionT682 -> T1480,\nX2708 -> T1480,\nX2709 -> s(0),\nX2710 -> s(s(s(s(s(s(0)))))),\nT683 -> T1481,\nX2711 -> T1481" }, { "from": 3037, "to": 3137, "label": "EVAL with clause\nlog2(X2730, X2731, X2732, X2732) :- ','(small(X2730), small(X2731)).\nand substitutionT682 -> T1484,\nX2730 -> T1484,\nX2731 -> s(s(s(0))),\nX2732 -> s(s(s(s(s(s(0)))))),\nT683 -> s(s(s(s(s(s(0))))))" }, { "from": 3037, "to": 3138, "label": "EVAL-BACKTRACK" }, { "from": 3089, "to": 3095, "label": "CASE" }, { "from": 3095, "to": 3096, "label": "PARALLEL" }, { "from": 3095, "to": 3097, "label": "PARALLEL" }, { "from": 3096, "to": 3098, "label": "EVAL with clause\nsmall(0).\nand substitutionT1480 -> 0" }, { "from": 3096, "to": 3099, "label": "EVAL-BACKTRACK" }, { "from": 3097, "to": 3102, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1480 -> s(0)" }, { "from": 3097, "to": 3103, "label": "EVAL-BACKTRACK" }, { "from": 3098, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(0)\nT782 -> T1481" }, { "from": 3102, "to": 1286, "label": "INSTANCE with matching:\nT781 -> s(0)\nT782 -> T1481" }, { "from": 3137, "to": 3139, "label": "CASE" }, { "from": 3139, "to": 3140, "label": "PARALLEL" }, { "from": 3139, "to": 3141, "label": "PARALLEL" }, { "from": 3140, "to": 3142, "label": "EVAL with clause\nsmall(0).\nand substitutionT1484 -> 0" }, { "from": 3140, "to": 3143, "label": "EVAL-BACKTRACK" }, { "from": 3141, "to": 3147, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1484 -> s(0)" }, { "from": 3141, "to": 3148, "label": "EVAL-BACKTRACK" }, { "from": 3142, "to": 3144, "label": "CASE" }, { "from": 3144, "to": 3145, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3145, "to": 3146, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3147, "to": 3149, "label": "CASE" }, { "from": 3149, "to": 3150, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3150, "to": 3151, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3167, "to": 3186, "label": "ONLY EVAL with clause\nlog2(X2757, s(s(X2758)), X2759, X2760) :- ','(small(X2757), log2(X2758, s(0), s(X2759), X2760)).\nand substitutionT670 -> T1493,\nX2757 -> T1493,\nX2758 -> 0,\nX2759 -> s(s(s(s(s(s(0)))))),\nT671 -> T1494,\nX2760 -> T1494" }, { "from": 3168, "to": 3219, "label": "EVAL with clause\nlog2(X2779, X2780, X2781, X2781) :- ','(small(X2779), small(X2780)).\nand substitutionT670 -> T1497,\nX2779 -> T1497,\nX2780 -> s(s(0)),\nX2781 -> s(s(s(s(s(s(0)))))),\nT671 -> s(s(s(s(s(s(0))))))" }, { "from": 3168, "to": 3220, "label": "EVAL-BACKTRACK" }, { "from": 3186, "to": 3187, "label": "CASE" }, { "from": 3187, "to": 3188, "label": "PARALLEL" }, { "from": 3187, "to": 3189, "label": "PARALLEL" }, { "from": 3188, "to": 3190, "label": "EVAL with clause\nsmall(0).\nand substitutionT1493 -> 0" }, { "from": 3188, "to": 3191, "label": "EVAL-BACKTRACK" }, { "from": 3189, "to": 3192, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1493 -> s(0)" }, { "from": 3189, "to": 3193, "label": "EVAL-BACKTRACK" }, { "from": 3190, "to": 1286, "label": "INSTANCE with matching:\nT781 -> 0\nT782 -> T1494" }, { "from": 3192, "to": 1286, "label": "INSTANCE with matching:\nT781 -> 0\nT782 -> T1494" }, { "from": 3219, "to": 3221, "label": "CASE" }, { "from": 3221, "to": 3222, "label": "PARALLEL" }, { "from": 3221, "to": 3223, "label": "PARALLEL" }, { "from": 3222, "to": 3224, "label": "EVAL with clause\nsmall(0).\nand substitutionT1497 -> 0" }, { "from": 3222, "to": 3225, "label": "EVAL-BACKTRACK" }, { "from": 3223, "to": 3229, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1497 -> s(0)" }, { "from": 3223, "to": 3230, "label": "EVAL-BACKTRACK" }, { "from": 3224, "to": 3226, "label": "CASE" }, { "from": 3226, "to": 3227, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3227, "to": 3228, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3229, "to": 3231, "label": "CASE" }, { "from": 3231, "to": 3232, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3232, "to": 3233, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3234, "to": 3292, "label": "EVAL with clause\nlog2(X2792, X2793, X2794, X2794) :- ','(small(X2792), small(X2793)).\nand substitutionT656 -> T1501,\nX2792 -> T1501,\nX2793 -> s(0),\nX2794 -> s(s(s(s(s(s(0)))))),\nT657 -> s(s(s(s(s(s(0))))))" }, { "from": 3234, "to": 3294, "label": "EVAL-BACKTRACK" }, { "from": 3292, "to": 3297, "label": "CASE" }, { "from": 3297, "to": 3299, "label": "PARALLEL" }, { "from": 3297, "to": 3300, "label": "PARALLEL" }, { "from": 3299, "to": 3306, "label": "EVAL with clause\nsmall(0).\nand substitutionT1501 -> 0" }, { "from": 3299, "to": 3307, "label": "EVAL-BACKTRACK" }, { "from": 3300, "to": 3312, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1501 -> s(0)" }, { "from": 3300, "to": 3313, "label": "EVAL-BACKTRACK" }, { "from": 3306, "to": 3308, "label": "CASE" }, { "from": 3308, "to": 3309, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3309, "to": 3310, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3310, "to": 3311, "label": "SUCCESS" }, { "from": 3312, "to": 3314, "label": "CASE" }, { "from": 3314, "to": 3315, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3315, "to": 3316, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3316, "to": 3317, "label": "SUCCESS" }, { "from": 3318, "to": 1094, "label": "INSTANCE" }, { "from": 3337, "to": 3339, "label": "CASE" }, { "from": 3339, "to": 3340, "label": "PARALLEL" }, { "from": 3339, "to": 3341, "label": "PARALLEL" }, { "from": 3340, "to": 3342, "label": "EVAL with clause\nsmall(0).\nand substitutionT1508 -> 0" }, { "from": 3340, "to": 3343, "label": "EVAL-BACKTRACK" }, { "from": 3341, "to": 3349, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1508 -> s(0)" }, { "from": 3341, "to": 3350, "label": "EVAL-BACKTRACK" }, { "from": 3342, "to": 3344, "label": "CASE" }, { "from": 3344, "to": 3345, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3345, "to": 3346, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1509 -> 0" }, { "from": 3345, "to": 3347, "label": "EVAL-BACKTRACK" }, { "from": 3346, "to": 3348, "label": "SUCCESS" }, { "from": 3349, "to": 3351, "label": "CASE" }, { "from": 3351, "to": 3352, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3352, "to": 3353, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1509 -> 0" }, { "from": 3352, "to": 3354, "label": "EVAL-BACKTRACK" }, { "from": 3353, "to": 3355, "label": "SUCCESS" }, { "from": 3358, "to": 3387, "label": "ONLY EVAL with clause\nlog2(X2832, s(s(X2833)), X2834, X2835) :- ','(small(X2832), log2(X2833, s(0), s(X2834), X2835)).\nand substitutionT605 -> T1520,\nX2832 -> T1520,\nX2833 -> s(s(s(s(s(0))))),\nX2834 -> s(s(s(s(s(0))))),\nT606 -> T1521,\nX2835 -> T1521" }, { "from": 3359, "to": 3411, "label": "EVAL with clause\nlog2(X2854, X2855, X2856, X2856) :- ','(small(X2854), small(X2855)).\nand substitutionT605 -> T1527,\nX2854 -> T1527,\nX2855 -> s(s(s(s(s(s(s(0))))))),\nX2856 -> s(s(s(s(s(0))))),\nT606 -> s(s(s(s(s(0)))))" }, { "from": 3359, "to": 3412, "label": "EVAL-BACKTRACK" }, { "from": 3387, "to": 3388, "label": "CASE" }, { "from": 3388, "to": 3389, "label": "PARALLEL" }, { "from": 3388, "to": 3390, "label": "PARALLEL" }, { "from": 3389, "to": 3391, "label": "EVAL with clause\nsmall(0).\nand substitutionT1520 -> 0" }, { "from": 3389, "to": 3392, "label": "EVAL-BACKTRACK" }, { "from": 3390, "to": 3407, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1520 -> s(0)" }, { "from": 3390, "to": 3408, "label": "EVAL-BACKTRACK" }, { "from": 3391, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(s(s(0)))))\nT657 -> T1521" }, { "from": 3407, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(s(s(0)))))\nT657 -> T1521" }, { "from": 3411, "to": 3413, "label": "CASE" }, { "from": 3413, "to": 3414, "label": "PARALLEL" }, { "from": 3413, "to": 3415, "label": "PARALLEL" }, { "from": 3414, "to": 3416, "label": "EVAL with clause\nsmall(0).\nand substitutionT1527 -> 0" }, { "from": 3414, "to": 3417, "label": "EVAL-BACKTRACK" }, { "from": 3415, "to": 3421, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1527 -> s(0)" }, { "from": 3415, "to": 3422, "label": "EVAL-BACKTRACK" }, { "from": 3416, "to": 3418, "label": "CASE" }, { "from": 3418, "to": 3419, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3419, "to": 3420, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3421, "to": 3423, "label": "CASE" }, { "from": 3423, "to": 3424, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3424, "to": 3425, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3428, "to": 3438, "label": "ONLY EVAL with clause\nlog2(X2881, s(s(X2882)), X2883, X2884) :- ','(small(X2881), log2(X2882, s(0), s(X2883), X2884)).\nand substitutionT593 -> T1538,\nX2881 -> T1538,\nX2882 -> s(s(s(s(0)))),\nX2883 -> s(s(s(s(s(0))))),\nT594 -> T1539,\nX2884 -> T1539" }, { "from": 3429, "to": 3511, "label": "EVAL with clause\nlog2(X2903, X2904, X2905, X2905) :- ','(small(X2903), small(X2904)).\nand substitutionT593 -> T1545,\nX2903 -> T1545,\nX2904 -> s(s(s(s(s(s(0)))))),\nX2905 -> s(s(s(s(s(0))))),\nT594 -> s(s(s(s(s(0)))))" }, { "from": 3429, "to": 3512, "label": "EVAL-BACKTRACK" }, { "from": 3438, "to": 3472, "label": "CASE" }, { "from": 3472, "to": 3473, "label": "PARALLEL" }, { "from": 3472, "to": 3474, "label": "PARALLEL" }, { "from": 3473, "to": 3475, "label": "EVAL with clause\nsmall(0).\nand substitutionT1538 -> 0" }, { "from": 3473, "to": 3476, "label": "EVAL-BACKTRACK" }, { "from": 3474, "to": 3494, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1538 -> s(0)" }, { "from": 3474, "to": 3495, "label": "EVAL-BACKTRACK" }, { "from": 3475, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(s(0))))\nT657 -> T1539" }, { "from": 3494, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(s(0))))\nT657 -> T1539" }, { "from": 3511, "to": 3513, "label": "CASE" }, { "from": 3513, "to": 3514, "label": "PARALLEL" }, { "from": 3513, "to": 3515, "label": "PARALLEL" }, { "from": 3514, "to": 3516, "label": "EVAL with clause\nsmall(0).\nand substitutionT1545 -> 0" }, { "from": 3514, "to": 3517, "label": "EVAL-BACKTRACK" }, { "from": 3515, "to": 3521, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1545 -> s(0)" }, { "from": 3515, "to": 3522, "label": "EVAL-BACKTRACK" }, { "from": 3516, "to": 3518, "label": "CASE" }, { "from": 3518, "to": 3519, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3519, "to": 3520, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3521, "to": 3523, "label": "CASE" }, { "from": 3523, "to": 3524, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3524, "to": 3525, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3547, "to": 3589, "label": "ONLY EVAL with clause\nlog2(X2930, s(s(X2931)), X2932, X2933) :- ','(small(X2930), log2(X2931, s(0), s(X2932), X2933)).\nand substitutionT581 -> T1556,\nX2930 -> T1556,\nX2931 -> s(s(s(0))),\nX2932 -> s(s(s(s(s(0))))),\nT582 -> T1557,\nX2933 -> T1557" }, { "from": 3548, "to": 3644, "label": "EVAL with clause\nlog2(X2952, X2953, X2954, X2954) :- ','(small(X2952), small(X2953)).\nand substitutionT581 -> T1563,\nX2952 -> T1563,\nX2953 -> s(s(s(s(s(0))))),\nX2954 -> s(s(s(s(s(0))))),\nT582 -> s(s(s(s(s(0)))))" }, { "from": 3548, "to": 3645, "label": "EVAL-BACKTRACK" }, { "from": 3589, "to": 3591, "label": "CASE" }, { "from": 3591, "to": 3592, "label": "PARALLEL" }, { "from": 3591, "to": 3593, "label": "PARALLEL" }, { "from": 3592, "to": 3594, "label": "EVAL with clause\nsmall(0).\nand substitutionT1556 -> 0" }, { "from": 3592, "to": 3595, "label": "EVAL-BACKTRACK" }, { "from": 3593, "to": 3627, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1556 -> s(0)" }, { "from": 3593, "to": 3628, "label": "EVAL-BACKTRACK" }, { "from": 3594, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(0)))\nT657 -> T1557" }, { "from": 3627, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(s(0)))\nT657 -> T1557" }, { "from": 3644, "to": 3646, "label": "CASE" }, { "from": 3646, "to": 3647, "label": "PARALLEL" }, { "from": 3646, "to": 3648, "label": "PARALLEL" }, { "from": 3647, "to": 3649, "label": "EVAL with clause\nsmall(0).\nand substitutionT1563 -> 0" }, { "from": 3647, "to": 3650, "label": "EVAL-BACKTRACK" }, { "from": 3648, "to": 3654, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1563 -> s(0)" }, { "from": 3648, "to": 3655, "label": "EVAL-BACKTRACK" }, { "from": 3649, "to": 3651, "label": "CASE" }, { "from": 3651, "to": 3652, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3652, "to": 3653, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3654, "to": 3656, "label": "CASE" }, { "from": 3656, "to": 3657, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3657, "to": 3658, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3677, "to": 3681, "label": "ONLY EVAL with clause\nlog2(X2979, s(s(X2980)), X2981, X2982) :- ','(small(X2979), log2(X2980, s(0), s(X2981), X2982)).\nand substitutionT569 -> T1574,\nX2979 -> T1574,\nX2980 -> s(s(0)),\nX2981 -> s(s(s(s(s(0))))),\nT570 -> T1575,\nX2982 -> T1575" }, { "from": 3678, "to": 3719, "label": "EVAL with clause\nlog2(X3001, X3002, X3003, X3003) :- ','(small(X3001), small(X3002)).\nand substitutionT569 -> T1581,\nX3001 -> T1581,\nX3002 -> s(s(s(s(0)))),\nX3003 -> s(s(s(s(s(0))))),\nT570 -> s(s(s(s(s(0)))))" }, { "from": 3678, "to": 3720, "label": "EVAL-BACKTRACK" }, { "from": 3681, "to": 3697, "label": "CASE" }, { "from": 3697, "to": 3698, "label": "PARALLEL" }, { "from": 3697, "to": 3699, "label": "PARALLEL" }, { "from": 3698, "to": 3700, "label": "EVAL with clause\nsmall(0).\nand substitutionT1574 -> 0" }, { "from": 3698, "to": 3701, "label": "EVAL-BACKTRACK" }, { "from": 3699, "to": 3702, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1574 -> s(0)" }, { "from": 3699, "to": 3703, "label": "EVAL-BACKTRACK" }, { "from": 3700, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(0))\nT657 -> T1575" }, { "from": 3702, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(s(0))\nT657 -> T1575" }, { "from": 3719, "to": 3721, "label": "CASE" }, { "from": 3721, "to": 3722, "label": "PARALLEL" }, { "from": 3721, "to": 3723, "label": "PARALLEL" }, { "from": 3722, "to": 3724, "label": "EVAL with clause\nsmall(0).\nand substitutionT1581 -> 0" }, { "from": 3722, "to": 3725, "label": "EVAL-BACKTRACK" }, { "from": 3723, "to": 3729, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1581 -> s(0)" }, { "from": 3723, "to": 3730, "label": "EVAL-BACKTRACK" }, { "from": 3724, "to": 3726, "label": "CASE" }, { "from": 3726, "to": 3727, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3727, "to": 3728, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3729, "to": 3731, "label": "CASE" }, { "from": 3731, "to": 3732, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3732, "to": 3733, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3736, "to": 3740, "label": "ONLY EVAL with clause\nlog2(X3028, s(s(X3029)), X3030, X3031) :- ','(small(X3028), log2(X3029, s(0), s(X3030), X3031)).\nand substitutionT557 -> T1590,\nX3028 -> T1590,\nX3029 -> s(0),\nX3030 -> s(s(s(s(s(0))))),\nT558 -> T1591,\nX3031 -> T1591" }, { "from": 3737, "to": 3754, "label": "EVAL with clause\nlog2(X3050, X3051, X3052, X3052) :- ','(small(X3050), small(X3051)).\nand substitutionT557 -> T1594,\nX3050 -> T1594,\nX3051 -> s(s(s(0))),\nX3052 -> s(s(s(s(s(0))))),\nT558 -> s(s(s(s(s(0)))))" }, { "from": 3737, "to": 3755, "label": "EVAL-BACKTRACK" }, { "from": 3740, "to": 3741, "label": "CASE" }, { "from": 3741, "to": 3742, "label": "PARALLEL" }, { "from": 3741, "to": 3743, "label": "PARALLEL" }, { "from": 3742, "to": 3744, "label": "EVAL with clause\nsmall(0).\nand substitutionT1590 -> 0" }, { "from": 3742, "to": 3745, "label": "EVAL-BACKTRACK" }, { "from": 3743, "to": 3746, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1590 -> s(0)" }, { "from": 3743, "to": 3747, "label": "EVAL-BACKTRACK" }, { "from": 3744, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(0)\nT657 -> T1591" }, { "from": 3746, "to": 1094, "label": "INSTANCE with matching:\nT656 -> s(0)\nT657 -> T1591" }, { "from": 3754, "to": 3756, "label": "CASE" }, { "from": 3756, "to": 3757, "label": "PARALLEL" }, { "from": 3756, "to": 3758, "label": "PARALLEL" }, { "from": 3757, "to": 3759, "label": "EVAL with clause\nsmall(0).\nand substitutionT1594 -> 0" }, { "from": 3757, "to": 3760, "label": "EVAL-BACKTRACK" }, { "from": 3758, "to": 3764, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1594 -> s(0)" }, { "from": 3758, "to": 3765, "label": "EVAL-BACKTRACK" }, { "from": 3759, "to": 3761, "label": "CASE" }, { "from": 3761, "to": 3762, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3762, "to": 3763, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3764, "to": 3766, "label": "CASE" }, { "from": 3766, "to": 3767, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3767, "to": 3768, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3772, "to": 3781, "label": "ONLY EVAL with clause\nlog2(X3077, s(s(X3078)), X3079, X3080) :- ','(small(X3077), log2(X3078, s(0), s(X3079), X3080)).\nand substitutionT545 -> T1603,\nX3077 -> T1603,\nX3078 -> 0,\nX3079 -> s(s(s(s(s(0))))),\nT546 -> T1604,\nX3080 -> T1604" }, { "from": 3773, "to": 3835, "label": "EVAL with clause\nlog2(X3099, X3100, X3101, X3101) :- ','(small(X3099), small(X3100)).\nand substitutionT545 -> T1607,\nX3099 -> T1607,\nX3100 -> s(s(0)),\nX3101 -> s(s(s(s(s(0))))),\nT546 -> s(s(s(s(s(0)))))" }, { "from": 3773, "to": 3836, "label": "EVAL-BACKTRACK" }, { "from": 3781, "to": 3782, "label": "CASE" }, { "from": 3782, "to": 3783, "label": "PARALLEL" }, { "from": 3782, "to": 3784, "label": "PARALLEL" }, { "from": 3783, "to": 3785, "label": "EVAL with clause\nsmall(0).\nand substitutionT1603 -> 0" }, { "from": 3783, "to": 3786, "label": "EVAL-BACKTRACK" }, { "from": 3784, "to": 3820, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1603 -> s(0)" }, { "from": 3784, "to": 3821, "label": "EVAL-BACKTRACK" }, { "from": 3785, "to": 1094, "label": "INSTANCE with matching:\nT656 -> 0\nT657 -> T1604" }, { "from": 3820, "to": 1094, "label": "INSTANCE with matching:\nT656 -> 0\nT657 -> T1604" }, { "from": 3835, "to": 3837, "label": "CASE" }, { "from": 3837, "to": 3838, "label": "PARALLEL" }, { "from": 3837, "to": 3839, "label": "PARALLEL" }, { "from": 3838, "to": 3840, "label": "EVAL with clause\nsmall(0).\nand substitutionT1607 -> 0" }, { "from": 3838, "to": 3841, "label": "EVAL-BACKTRACK" }, { "from": 3839, "to": 3845, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1607 -> s(0)" }, { "from": 3839, "to": 3846, "label": "EVAL-BACKTRACK" }, { "from": 3840, "to": 3842, "label": "CASE" }, { "from": 3842, "to": 3843, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3843, "to": 3844, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3845, "to": 3847, "label": "CASE" }, { "from": 3847, "to": 3848, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3848, "to": 3849, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3850, "to": 3901, "label": "EVAL with clause\nlog2(X3112, X3113, X3114, X3114) :- ','(small(X3112), small(X3113)).\nand substitutionT531 -> T1611,\nX3112 -> T1611,\nX3113 -> s(0),\nX3114 -> s(s(s(s(s(0))))),\nT532 -> s(s(s(s(s(0)))))" }, { "from": 3850, "to": 3902, "label": "EVAL-BACKTRACK" }, { "from": 3901, "to": 3903, "label": "CASE" }, { "from": 3903, "to": 3904, "label": "PARALLEL" }, { "from": 3903, "to": 3905, "label": "PARALLEL" }, { "from": 3904, "to": 3906, "label": "EVAL with clause\nsmall(0).\nand substitutionT1611 -> 0" }, { "from": 3904, "to": 3907, "label": "EVAL-BACKTRACK" }, { "from": 3905, "to": 3912, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1611 -> s(0)" }, { "from": 3905, "to": 3913, "label": "EVAL-BACKTRACK" }, { "from": 3906, "to": 3908, "label": "CASE" }, { "from": 3908, "to": 3909, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3909, "to": 3910, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3910, "to": 3911, "label": "SUCCESS" }, { "from": 3912, "to": 3914, "label": "CASE" }, { "from": 3914, "to": 3915, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3915, "to": 3916, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3916, "to": 3917, "label": "SUCCESS" }, { "from": 3918, "to": 931, "label": "INSTANCE" }, { "from": 3953, "to": 3955, "label": "CASE" }, { "from": 3955, "to": 3956, "label": "PARALLEL" }, { "from": 3955, "to": 3957, "label": "PARALLEL" }, { "from": 3956, "to": 3958, "label": "EVAL with clause\nsmall(0).\nand substitutionT1618 -> 0" }, { "from": 3956, "to": 3959, "label": "EVAL-BACKTRACK" }, { "from": 3957, "to": 3967, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1618 -> s(0)" }, { "from": 3957, "to": 3968, "label": "EVAL-BACKTRACK" }, { "from": 3958, "to": 3960, "label": "CASE" }, { "from": 3960, "to": 3961, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3961, "to": 3962, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1619 -> 0" }, { "from": 3961, "to": 3964, "label": "EVAL-BACKTRACK" }, { "from": 3962, "to": 3966, "label": "SUCCESS" }, { "from": 3967, "to": 3969, "label": "CASE" }, { "from": 3969, "to": 3970, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3970, "to": 3971, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1619 -> 0" }, { "from": 3970, "to": 3972, "label": "EVAL-BACKTRACK" }, { "from": 3971, "to": 3973, "label": "SUCCESS" }, { "from": 3989, "to": 4001, "label": "ONLY EVAL with clause\nlog2(X3152, s(s(X3153)), X3154, X3155) :- ','(small(X3152), log2(X3153, s(0), s(X3154), X3155)).\nand substitutionT480 -> T1630,\nX3152 -> T1630,\nX3153 -> s(s(s(s(s(0))))),\nX3154 -> s(s(s(s(0)))),\nT481 -> T1631,\nX3155 -> T1631" }, { "from": 3990, "to": 4052, "label": "EVAL with clause\nlog2(X3174, X3175, X3176, X3176) :- ','(small(X3174), small(X3175)).\nand substitutionT480 -> T1637,\nX3174 -> T1637,\nX3175 -> s(s(s(s(s(s(s(0))))))),\nX3176 -> s(s(s(s(0)))),\nT481 -> s(s(s(s(0))))" }, { "from": 3990, "to": 4053, "label": "EVAL-BACKTRACK" }, { "from": 4001, "to": 4002, "label": "CASE" }, { "from": 4002, "to": 4003, "label": "PARALLEL" }, { "from": 4002, "to": 4004, "label": "PARALLEL" }, { "from": 4003, "to": 4005, "label": "EVAL with clause\nsmall(0).\nand substitutionT1630 -> 0" }, { "from": 4003, "to": 4006, "label": "EVAL-BACKTRACK" }, { "from": 4004, "to": 4023, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1630 -> s(0)" }, { "from": 4004, "to": 4024, "label": "EVAL-BACKTRACK" }, { "from": 4005, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(s(s(0)))))\nT532 -> T1631" }, { "from": 4023, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(s(s(0)))))\nT532 -> T1631" }, { "from": 4052, "to": 4054, "label": "CASE" }, { "from": 4054, "to": 4055, "label": "PARALLEL" }, { "from": 4054, "to": 4056, "label": "PARALLEL" }, { "from": 4055, "to": 4057, "label": "EVAL with clause\nsmall(0).\nand substitutionT1637 -> 0" }, { "from": 4055, "to": 4058, "label": "EVAL-BACKTRACK" }, { "from": 4056, "to": 4062, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1637 -> s(0)" }, { "from": 4056, "to": 4063, "label": "EVAL-BACKTRACK" }, { "from": 4057, "to": 4059, "label": "CASE" }, { "from": 4059, "to": 4060, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4060, "to": 4061, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4062, "to": 4064, "label": "CASE" }, { "from": 4064, "to": 4065, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4065, "to": 4066, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4082, "to": 4107, "label": "ONLY EVAL with clause\nlog2(X3201, s(s(X3202)), X3203, X3204) :- ','(small(X3201), log2(X3202, s(0), s(X3203), X3204)).\nand substitutionT468 -> T1648,\nX3201 -> T1648,\nX3202 -> s(s(s(s(0)))),\nX3203 -> s(s(s(s(0)))),\nT469 -> T1649,\nX3204 -> T1649" }, { "from": 4083, "to": 4131, "label": "EVAL with clause\nlog2(X3223, X3224, X3225, X3225) :- ','(small(X3223), small(X3224)).\nand substitutionT468 -> T1655,\nX3223 -> T1655,\nX3224 -> s(s(s(s(s(s(0)))))),\nX3225 -> s(s(s(s(0)))),\nT469 -> s(s(s(s(0))))" }, { "from": 4083, "to": 4132, "label": "EVAL-BACKTRACK" }, { "from": 4107, "to": 4108, "label": "CASE" }, { "from": 4108, "to": 4109, "label": "PARALLEL" }, { "from": 4108, "to": 4110, "label": "PARALLEL" }, { "from": 4109, "to": 4111, "label": "EVAL with clause\nsmall(0).\nand substitutionT1648 -> 0" }, { "from": 4109, "to": 4112, "label": "EVAL-BACKTRACK" }, { "from": 4110, "to": 4114, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1648 -> s(0)" }, { "from": 4110, "to": 4115, "label": "EVAL-BACKTRACK" }, { "from": 4111, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(s(0))))\nT532 -> T1649" }, { "from": 4114, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(s(0))))\nT532 -> T1649" }, { "from": 4131, "to": 4133, "label": "CASE" }, { "from": 4133, "to": 4134, "label": "PARALLEL" }, { "from": 4133, "to": 4135, "label": "PARALLEL" }, { "from": 4134, "to": 4136, "label": "EVAL with clause\nsmall(0).\nand substitutionT1655 -> 0" }, { "from": 4134, "to": 4137, "label": "EVAL-BACKTRACK" }, { "from": 4135, "to": 4141, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1655 -> s(0)" }, { "from": 4135, "to": 4142, "label": "EVAL-BACKTRACK" }, { "from": 4136, "to": 4138, "label": "CASE" }, { "from": 4138, "to": 4139, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4139, "to": 4140, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4141, "to": 4143, "label": "CASE" }, { "from": 4143, "to": 4144, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4144, "to": 4145, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4176, "to": 4183, "label": "ONLY EVAL with clause\nlog2(X3250, s(s(X3251)), X3252, X3253) :- ','(small(X3250), log2(X3251, s(0), s(X3252), X3253)).\nand substitutionT456 -> T1666,\nX3250 -> T1666,\nX3251 -> s(s(s(0))),\nX3252 -> s(s(s(s(0)))),\nT457 -> T1667,\nX3253 -> T1667" }, { "from": 4177, "to": 4228, "label": "EVAL with clause\nlog2(X3272, X3273, X3274, X3274) :- ','(small(X3272), small(X3273)).\nand substitutionT456 -> T1673,\nX3272 -> T1673,\nX3273 -> s(s(s(s(s(0))))),\nX3274 -> s(s(s(s(0)))),\nT457 -> s(s(s(s(0))))" }, { "from": 4177, "to": 4230, "label": "EVAL-BACKTRACK" }, { "from": 4183, "to": 4195, "label": "CASE" }, { "from": 4195, "to": 4196, "label": "PARALLEL" }, { "from": 4195, "to": 4197, "label": "PARALLEL" }, { "from": 4196, "to": 4198, "label": "EVAL with clause\nsmall(0).\nand substitutionT1666 -> 0" }, { "from": 4196, "to": 4199, "label": "EVAL-BACKTRACK" }, { "from": 4197, "to": 4204, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1666 -> s(0)" }, { "from": 4197, "to": 4205, "label": "EVAL-BACKTRACK" }, { "from": 4198, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(0)))\nT532 -> T1667" }, { "from": 4204, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(s(0)))\nT532 -> T1667" }, { "from": 4228, "to": 4233, "label": "CASE" }, { "from": 4233, "to": 4236, "label": "PARALLEL" }, { "from": 4233, "to": 4237, "label": "PARALLEL" }, { "from": 4236, "to": 4240, "label": "EVAL with clause\nsmall(0).\nand substitutionT1673 -> 0" }, { "from": 4236, "to": 4242, "label": "EVAL-BACKTRACK" }, { "from": 4237, "to": 4246, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1673 -> s(0)" }, { "from": 4237, "to": 4247, "label": "EVAL-BACKTRACK" }, { "from": 4240, "to": 4243, "label": "CASE" }, { "from": 4243, "to": 4244, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4244, "to": 4245, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4246, "to": 4248, "label": "CASE" }, { "from": 4248, "to": 4249, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4249, "to": 4250, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4255, "to": 4264, "label": "ONLY EVAL with clause\nlog2(X3299, s(s(X3300)), X3301, X3302) :- ','(small(X3299), log2(X3300, s(0), s(X3301), X3302)).\nand substitutionT444 -> T1684,\nX3299 -> T1684,\nX3300 -> s(s(0)),\nX3301 -> s(s(s(s(0)))),\nT445 -> T1685,\nX3302 -> T1685" }, { "from": 4256, "to": 4311, "label": "EVAL with clause\nlog2(X3321, X3322, X3323, X3323) :- ','(small(X3321), small(X3322)).\nand substitutionT444 -> T1691,\nX3321 -> T1691,\nX3322 -> s(s(s(s(0)))),\nX3323 -> s(s(s(s(0)))),\nT445 -> s(s(s(s(0))))" }, { "from": 4256, "to": 4312, "label": "EVAL-BACKTRACK" }, { "from": 4264, "to": 4272, "label": "CASE" }, { "from": 4272, "to": 4273, "label": "PARALLEL" }, { "from": 4272, "to": 4274, "label": "PARALLEL" }, { "from": 4273, "to": 4275, "label": "EVAL with clause\nsmall(0).\nand substitutionT1684 -> 0" }, { "from": 4273, "to": 4276, "label": "EVAL-BACKTRACK" }, { "from": 4274, "to": 4279, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1684 -> s(0)" }, { "from": 4274, "to": 4280, "label": "EVAL-BACKTRACK" }, { "from": 4275, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(0))\nT532 -> T1685" }, { "from": 4279, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(s(0))\nT532 -> T1685" }, { "from": 4311, "to": 4313, "label": "CASE" }, { "from": 4313, "to": 4314, "label": "PARALLEL" }, { "from": 4313, "to": 4315, "label": "PARALLEL" }, { "from": 4314, "to": 4316, "label": "EVAL with clause\nsmall(0).\nand substitutionT1691 -> 0" }, { "from": 4314, "to": 4317, "label": "EVAL-BACKTRACK" }, { "from": 4315, "to": 4321, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1691 -> s(0)" }, { "from": 4315, "to": 4322, "label": "EVAL-BACKTRACK" }, { "from": 4316, "to": 4318, "label": "CASE" }, { "from": 4318, "to": 4319, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4319, "to": 4320, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4321, "to": 4323, "label": "CASE" }, { "from": 4323, "to": 4324, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4324, "to": 4325, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4330, "to": 4344, "label": "ONLY EVAL with clause\nlog2(X3348, s(s(X3349)), X3350, X3351) :- ','(small(X3348), log2(X3349, s(0), s(X3350), X3351)).\nand substitutionT432 -> T1700,\nX3348 -> T1700,\nX3349 -> s(0),\nX3350 -> s(s(s(s(0)))),\nT433 -> T1701,\nX3351 -> T1701" }, { "from": 4331, "to": 4387, "label": "EVAL with clause\nlog2(X3370, X3371, X3372, X3372) :- ','(small(X3370), small(X3371)).\nand substitutionT432 -> T1704,\nX3370 -> T1704,\nX3371 -> s(s(s(0))),\nX3372 -> s(s(s(s(0)))),\nT433 -> s(s(s(s(0))))" }, { "from": 4331, "to": 4388, "label": "EVAL-BACKTRACK" }, { "from": 4344, "to": 4345, "label": "CASE" }, { "from": 4345, "to": 4346, "label": "PARALLEL" }, { "from": 4345, "to": 4347, "label": "PARALLEL" }, { "from": 4346, "to": 4351, "label": "EVAL with clause\nsmall(0).\nand substitutionT1700 -> 0" }, { "from": 4346, "to": 4353, "label": "EVAL-BACKTRACK" }, { "from": 4347, "to": 4354, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1700 -> s(0)" }, { "from": 4347, "to": 4355, "label": "EVAL-BACKTRACK" }, { "from": 4351, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(0)\nT532 -> T1701" }, { "from": 4354, "to": 931, "label": "INSTANCE with matching:\nT531 -> s(0)\nT532 -> T1701" }, { "from": 4387, "to": 4389, "label": "CASE" }, { "from": 4389, "to": 4390, "label": "PARALLEL" }, { "from": 4389, "to": 4391, "label": "PARALLEL" }, { "from": 4390, "to": 4392, "label": "EVAL with clause\nsmall(0).\nand substitutionT1704 -> 0" }, { "from": 4390, "to": 4393, "label": "EVAL-BACKTRACK" }, { "from": 4391, "to": 4397, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1704 -> s(0)" }, { "from": 4391, "to": 4398, "label": "EVAL-BACKTRACK" }, { "from": 4392, "to": 4394, "label": "CASE" }, { "from": 4394, "to": 4395, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4395, "to": 4396, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4397, "to": 4399, "label": "CASE" }, { "from": 4399, "to": 4400, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4400, "to": 4401, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4423, "to": 4452, "label": "ONLY EVAL with clause\nlog2(X3397, s(s(X3398)), X3399, X3400) :- ','(small(X3397), log2(X3398, s(0), s(X3399), X3400)).\nand substitutionT420 -> T1713,\nX3397 -> T1713,\nX3398 -> 0,\nX3399 -> s(s(s(s(0)))),\nT421 -> T1714,\nX3400 -> T1714" }, { "from": 4424, "to": 4480, "label": "EVAL with clause\nlog2(X3419, X3420, X3421, X3421) :- ','(small(X3419), small(X3420)).\nand substitutionT420 -> T1717,\nX3419 -> T1717,\nX3420 -> s(s(0)),\nX3421 -> s(s(s(s(0)))),\nT421 -> s(s(s(s(0))))" }, { "from": 4424, "to": 4481, "label": "EVAL-BACKTRACK" }, { "from": 4452, "to": 4453, "label": "CASE" }, { "from": 4453, "to": 4454, "label": "PARALLEL" }, { "from": 4453, "to": 4455, "label": "PARALLEL" }, { "from": 4454, "to": 4456, "label": "EVAL with clause\nsmall(0).\nand substitutionT1713 -> 0" }, { "from": 4454, "to": 4457, "label": "EVAL-BACKTRACK" }, { "from": 4455, "to": 4460, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1713 -> s(0)" }, { "from": 4455, "to": 4461, "label": "EVAL-BACKTRACK" }, { "from": 4456, "to": 931, "label": "INSTANCE with matching:\nT531 -> 0\nT532 -> T1714" }, { "from": 4460, "to": 931, "label": "INSTANCE with matching:\nT531 -> 0\nT532 -> T1714" }, { "from": 4480, "to": 4482, "label": "CASE" }, { "from": 4482, "to": 4483, "label": "PARALLEL" }, { "from": 4482, "to": 4484, "label": "PARALLEL" }, { "from": 4483, "to": 4485, "label": "EVAL with clause\nsmall(0).\nand substitutionT1717 -> 0" }, { "from": 4483, "to": 4486, "label": "EVAL-BACKTRACK" }, { "from": 4484, "to": 4490, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1717 -> s(0)" }, { "from": 4484, "to": 4491, "label": "EVAL-BACKTRACK" }, { "from": 4485, "to": 4487, "label": "CASE" }, { "from": 4487, "to": 4488, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4488, "to": 4489, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4490, "to": 4492, "label": "CASE" }, { "from": 4492, "to": 4493, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4493, "to": 4494, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4500, "to": 4504, "label": "EVAL with clause\nlog2(X3432, X3433, X3434, X3434) :- ','(small(X3432), small(X3433)).\nand substitutionT406 -> T1721,\nX3432 -> T1721,\nX3433 -> s(0),\nX3434 -> s(s(s(s(0)))),\nT407 -> s(s(s(s(0))))" }, { "from": 4500, "to": 4505, "label": "EVAL-BACKTRACK" }, { "from": 4504, "to": 4506, "label": "CASE" }, { "from": 4506, "to": 4507, "label": "PARALLEL" }, { "from": 4506, "to": 4508, "label": "PARALLEL" }, { "from": 4507, "to": 4509, "label": "EVAL with clause\nsmall(0).\nand substitutionT1721 -> 0" }, { "from": 4507, "to": 4510, "label": "EVAL-BACKTRACK" }, { "from": 4508, "to": 4515, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1721 -> s(0)" }, { "from": 4508, "to": 4516, "label": "EVAL-BACKTRACK" }, { "from": 4509, "to": 4511, "label": "CASE" }, { "from": 4511, "to": 4512, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4512, "to": 4513, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4513, "to": 4514, "label": "SUCCESS" }, { "from": 4515, "to": 4517, "label": "CASE" }, { "from": 4517, "to": 4518, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4518, "to": 4519, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4519, "to": 4520, "label": "SUCCESS" }, { "from": 4521, "to": 786, "label": "INSTANCE" }, { "from": 4545, "to": 4547, "label": "CASE" }, { "from": 4547, "to": 4548, "label": "PARALLEL" }, { "from": 4547, "to": 4549, "label": "PARALLEL" }, { "from": 4548, "to": 4550, "label": "EVAL with clause\nsmall(0).\nand substitutionT1728 -> 0" }, { "from": 4548, "to": 4551, "label": "EVAL-BACKTRACK" }, { "from": 4549, "to": 4557, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1728 -> s(0)" }, { "from": 4549, "to": 4558, "label": "EVAL-BACKTRACK" }, { "from": 4550, "to": 4552, "label": "CASE" }, { "from": 4552, "to": 4553, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4553, "to": 4554, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1729 -> 0" }, { "from": 4553, "to": 4555, "label": "EVAL-BACKTRACK" }, { "from": 4554, "to": 4556, "label": "SUCCESS" }, { "from": 4557, "to": 4559, "label": "CASE" }, { "from": 4559, "to": 4560, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4560, "to": 4561, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1729 -> 0" }, { "from": 4560, "to": 4562, "label": "EVAL-BACKTRACK" }, { "from": 4561, "to": 4563, "label": "SUCCESS" }, { "from": 4582, "to": 4611, "label": "ONLY EVAL with clause\nlog2(X3472, s(s(X3473)), X3474, X3475) :- ','(small(X3472), log2(X3473, s(0), s(X3474), X3475)).\nand substitutionT355 -> T1740,\nX3472 -> T1740,\nX3473 -> s(s(s(s(s(0))))),\nX3474 -> s(s(s(0))),\nT356 -> T1741,\nX3475 -> T1741" }, { "from": 4583, "to": 4655, "label": "EVAL with clause\nlog2(X3494, X3495, X3496, X3496) :- ','(small(X3494), small(X3495)).\nand substitutionT355 -> T1747,\nX3494 -> T1747,\nX3495 -> s(s(s(s(s(s(s(0))))))),\nX3496 -> s(s(s(0))),\nT356 -> s(s(s(0)))" }, { "from": 4583, "to": 4656, "label": "EVAL-BACKTRACK" }, { "from": 4611, "to": 4631, "label": "CASE" }, { "from": 4631, "to": 4632, "label": "PARALLEL" }, { "from": 4631, "to": 4633, "label": "PARALLEL" }, { "from": 4632, "to": 4634, "label": "EVAL with clause\nsmall(0).\nand substitutionT1740 -> 0" }, { "from": 4632, "to": 4635, "label": "EVAL-BACKTRACK" }, { "from": 4633, "to": 4636, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1740 -> s(0)" }, { "from": 4633, "to": 4637, "label": "EVAL-BACKTRACK" }, { "from": 4634, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(s(s(0)))))\nT407 -> T1741" }, { "from": 4636, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(s(s(0)))))\nT407 -> T1741" }, { "from": 4655, "to": 4657, "label": "CASE" }, { "from": 4657, "to": 4658, "label": "PARALLEL" }, { "from": 4657, "to": 4659, "label": "PARALLEL" }, { "from": 4658, "to": 4660, "label": "EVAL with clause\nsmall(0).\nand substitutionT1747 -> 0" }, { "from": 4658, "to": 4661, "label": "EVAL-BACKTRACK" }, { "from": 4659, "to": 4665, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1747 -> s(0)" }, { "from": 4659, "to": 4666, "label": "EVAL-BACKTRACK" }, { "from": 4660, "to": 4662, "label": "CASE" }, { "from": 4662, "to": 4663, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4663, "to": 4664, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4665, "to": 4667, "label": "CASE" }, { "from": 4667, "to": 4668, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4668, "to": 4669, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4678, "to": 4701, "label": "ONLY EVAL with clause\nlog2(X3521, s(s(X3522)), X3523, X3524) :- ','(small(X3521), log2(X3522, s(0), s(X3523), X3524)).\nand substitutionT343 -> T1758,\nX3521 -> T1758,\nX3522 -> s(s(s(s(0)))),\nX3523 -> s(s(s(0))),\nT344 -> T1759,\nX3524 -> T1759" }, { "from": 4679, "to": 4730, "label": "EVAL with clause\nlog2(X3543, X3544, X3545, X3545) :- ','(small(X3543), small(X3544)).\nand substitutionT343 -> T1765,\nX3543 -> T1765,\nX3544 -> s(s(s(s(s(s(0)))))),\nX3545 -> s(s(s(0))),\nT344 -> s(s(s(0)))" }, { "from": 4679, "to": 4731, "label": "EVAL-BACKTRACK" }, { "from": 4701, "to": 4706, "label": "CASE" }, { "from": 4706, "to": 4707, "label": "PARALLEL" }, { "from": 4706, "to": 4708, "label": "PARALLEL" }, { "from": 4707, "to": 4709, "label": "EVAL with clause\nsmall(0).\nand substitutionT1758 -> 0" }, { "from": 4707, "to": 4710, "label": "EVAL-BACKTRACK" }, { "from": 4708, "to": 4711, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1758 -> s(0)" }, { "from": 4708, "to": 4712, "label": "EVAL-BACKTRACK" }, { "from": 4709, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(s(0))))\nT407 -> T1759" }, { "from": 4711, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(s(0))))\nT407 -> T1759" }, { "from": 4730, "to": 4732, "label": "CASE" }, { "from": 4732, "to": 4733, "label": "PARALLEL" }, { "from": 4732, "to": 4734, "label": "PARALLEL" }, { "from": 4733, "to": 4735, "label": "EVAL with clause\nsmall(0).\nand substitutionT1765 -> 0" }, { "from": 4733, "to": 4736, "label": "EVAL-BACKTRACK" }, { "from": 4734, "to": 4740, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1765 -> s(0)" }, { "from": 4734, "to": 4741, "label": "EVAL-BACKTRACK" }, { "from": 4735, "to": 4737, "label": "CASE" }, { "from": 4737, "to": 4738, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4738, "to": 4739, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4740, "to": 4742, "label": "CASE" }, { "from": 4742, "to": 4743, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4743, "to": 4744, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4753, "to": 4778, "label": "ONLY EVAL with clause\nlog2(X3570, s(s(X3571)), X3572, X3573) :- ','(small(X3570), log2(X3571, s(0), s(X3572), X3573)).\nand substitutionT331 -> T1776,\nX3570 -> T1776,\nX3571 -> s(s(s(0))),\nX3572 -> s(s(s(0))),\nT332 -> T1777,\nX3573 -> T1777" }, { "from": 4754, "to": 4805, "label": "EVAL with clause\nlog2(X3592, X3593, X3594, X3594) :- ','(small(X3592), small(X3593)).\nand substitutionT331 -> T1783,\nX3592 -> T1783,\nX3593 -> s(s(s(s(s(0))))),\nX3594 -> s(s(s(0))),\nT332 -> s(s(s(0)))" }, { "from": 4754, "to": 4806, "label": "EVAL-BACKTRACK" }, { "from": 4778, "to": 4781, "label": "CASE" }, { "from": 4781, "to": 4782, "label": "PARALLEL" }, { "from": 4781, "to": 4783, "label": "PARALLEL" }, { "from": 4782, "to": 4784, "label": "EVAL with clause\nsmall(0).\nand substitutionT1776 -> 0" }, { "from": 4782, "to": 4785, "label": "EVAL-BACKTRACK" }, { "from": 4783, "to": 4786, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1776 -> s(0)" }, { "from": 4783, "to": 4787, "label": "EVAL-BACKTRACK" }, { "from": 4784, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(0)))\nT407 -> T1777" }, { "from": 4786, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(s(0)))\nT407 -> T1777" }, { "from": 4805, "to": 4807, "label": "CASE" }, { "from": 4807, "to": 4808, "label": "PARALLEL" }, { "from": 4807, "to": 4809, "label": "PARALLEL" }, { "from": 4808, "to": 4810, "label": "EVAL with clause\nsmall(0).\nand substitutionT1783 -> 0" }, { "from": 4808, "to": 4811, "label": "EVAL-BACKTRACK" }, { "from": 4809, "to": 4815, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1783 -> s(0)" }, { "from": 4809, "to": 4816, "label": "EVAL-BACKTRACK" }, { "from": 4810, "to": 4812, "label": "CASE" }, { "from": 4812, "to": 4813, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4813, "to": 4814, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4815, "to": 4817, "label": "CASE" }, { "from": 4817, "to": 4818, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4818, "to": 4819, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4828, "to": 4853, "label": "ONLY EVAL with clause\nlog2(X3619, s(s(X3620)), X3621, X3622) :- ','(small(X3619), log2(X3620, s(0), s(X3621), X3622)).\nand substitutionT319 -> T1794,\nX3619 -> T1794,\nX3620 -> s(s(0)),\nX3621 -> s(s(s(0))),\nT320 -> T1795,\nX3622 -> T1795" }, { "from": 4829, "to": 4880, "label": "EVAL with clause\nlog2(X3641, X3642, X3643, X3643) :- ','(small(X3641), small(X3642)).\nand substitutionT319 -> T1801,\nX3641 -> T1801,\nX3642 -> s(s(s(s(0)))),\nX3643 -> s(s(s(0))),\nT320 -> s(s(s(0)))" }, { "from": 4829, "to": 4881, "label": "EVAL-BACKTRACK" }, { "from": 4853, "to": 4856, "label": "CASE" }, { "from": 4856, "to": 4857, "label": "PARALLEL" }, { "from": 4856, "to": 4858, "label": "PARALLEL" }, { "from": 4857, "to": 4859, "label": "EVAL with clause\nsmall(0).\nand substitutionT1794 -> 0" }, { "from": 4857, "to": 4860, "label": "EVAL-BACKTRACK" }, { "from": 4858, "to": 4861, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1794 -> s(0)" }, { "from": 4858, "to": 4862, "label": "EVAL-BACKTRACK" }, { "from": 4859, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(0))\nT407 -> T1795" }, { "from": 4861, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(s(0))\nT407 -> T1795" }, { "from": 4880, "to": 4882, "label": "CASE" }, { "from": 4882, "to": 4883, "label": "PARALLEL" }, { "from": 4882, "to": 4884, "label": "PARALLEL" }, { "from": 4883, "to": 4885, "label": "EVAL with clause\nsmall(0).\nand substitutionT1801 -> 0" }, { "from": 4883, "to": 4886, "label": "EVAL-BACKTRACK" }, { "from": 4884, "to": 4890, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1801 -> s(0)" }, { "from": 4884, "to": 4891, "label": "EVAL-BACKTRACK" }, { "from": 4885, "to": 4887, "label": "CASE" }, { "from": 4887, "to": 4888, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4888, "to": 4889, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4890, "to": 4892, "label": "CASE" }, { "from": 4892, "to": 4893, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4893, "to": 4894, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4903, "to": 4928, "label": "ONLY EVAL with clause\nlog2(X3668, s(s(X3669)), X3670, X3671) :- ','(small(X3668), log2(X3669, s(0), s(X3670), X3671)).\nand substitutionT307 -> T1810,\nX3668 -> T1810,\nX3669 -> s(0),\nX3670 -> s(s(s(0))),\nT308 -> T1811,\nX3671 -> T1811" }, { "from": 4904, "to": 4955, "label": "EVAL with clause\nlog2(X3690, X3691, X3692, X3692) :- ','(small(X3690), small(X3691)).\nand substitutionT307 -> T1814,\nX3690 -> T1814,\nX3691 -> s(s(s(0))),\nX3692 -> s(s(s(0))),\nT308 -> s(s(s(0)))" }, { "from": 4904, "to": 4956, "label": "EVAL-BACKTRACK" }, { "from": 4928, "to": 4929, "label": "CASE" }, { "from": 4929, "to": 4932, "label": "PARALLEL" }, { "from": 4929, "to": 4933, "label": "PARALLEL" }, { "from": 4932, "to": 4934, "label": "EVAL with clause\nsmall(0).\nand substitutionT1810 -> 0" }, { "from": 4932, "to": 4935, "label": "EVAL-BACKTRACK" }, { "from": 4933, "to": 4936, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1810 -> s(0)" }, { "from": 4933, "to": 4937, "label": "EVAL-BACKTRACK" }, { "from": 4934, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(0)\nT407 -> T1811" }, { "from": 4936, "to": 786, "label": "INSTANCE with matching:\nT406 -> s(0)\nT407 -> T1811" }, { "from": 4955, "to": 4957, "label": "CASE" }, { "from": 4957, "to": 4958, "label": "PARALLEL" }, { "from": 4957, "to": 4959, "label": "PARALLEL" }, { "from": 4958, "to": 4960, "label": "EVAL with clause\nsmall(0).\nand substitutionT1814 -> 0" }, { "from": 4958, "to": 4961, "label": "EVAL-BACKTRACK" }, { "from": 4959, "to": 4965, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1814 -> s(0)" }, { "from": 4959, "to": 4967, "label": "EVAL-BACKTRACK" }, { "from": 4960, "to": 4962, "label": "CASE" }, { "from": 4962, "to": 4963, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4963, "to": 4964, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4965, "to": 4968, "label": "CASE" }, { "from": 4968, "to": 4969, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4969, "to": 4970, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4998, "to": 5015, "label": "ONLY EVAL with clause\nlog2(X3717, s(s(X3718)), X3719, X3720) :- ','(small(X3717), log2(X3718, s(0), s(X3719), X3720)).\nand substitutionT295 -> T1823,\nX3717 -> T1823,\nX3718 -> 0,\nX3719 -> s(s(s(0))),\nT296 -> T1824,\nX3720 -> T1824" }, { "from": 4999, "to": 5046, "label": "EVAL with clause\nlog2(X3739, X3740, X3741, X3741) :- ','(small(X3739), small(X3740)).\nand substitutionT295 -> T1827,\nX3739 -> T1827,\nX3740 -> s(s(0)),\nX3741 -> s(s(s(0))),\nT296 -> s(s(s(0)))" }, { "from": 4999, "to": 5047, "label": "EVAL-BACKTRACK" }, { "from": 5015, "to": 5035, "label": "CASE" }, { "from": 5035, "to": 5036, "label": "PARALLEL" }, { "from": 5035, "to": 5037, "label": "PARALLEL" }, { "from": 5036, "to": 5038, "label": "EVAL with clause\nsmall(0).\nand substitutionT1823 -> 0" }, { "from": 5036, "to": 5039, "label": "EVAL-BACKTRACK" }, { "from": 5037, "to": 5040, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1823 -> s(0)" }, { "from": 5037, "to": 5041, "label": "EVAL-BACKTRACK" }, { "from": 5038, "to": 786, "label": "INSTANCE with matching:\nT406 -> 0\nT407 -> T1824" }, { "from": 5040, "to": 786, "label": "INSTANCE with matching:\nT406 -> 0\nT407 -> T1824" }, { "from": 5046, "to": 5048, "label": "CASE" }, { "from": 5048, "to": 5049, "label": "PARALLEL" }, { "from": 5048, "to": 5050, "label": "PARALLEL" }, { "from": 5049, "to": 5051, "label": "EVAL with clause\nsmall(0).\nand substitutionT1827 -> 0" }, { "from": 5049, "to": 5052, "label": "EVAL-BACKTRACK" }, { "from": 5050, "to": 5056, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1827 -> s(0)" }, { "from": 5050, "to": 5057, "label": "EVAL-BACKTRACK" }, { "from": 5051, "to": 5053, "label": "CASE" }, { "from": 5053, "to": 5054, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5054, "to": 5055, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5056, "to": 5058, "label": "CASE" }, { "from": 5058, "to": 5059, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5059, "to": 5060, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5062, "to": 5071, "label": "EVAL with clause\nlog2(X3752, X3753, X3754, X3754) :- ','(small(X3752), small(X3753)).\nand substitutionT281 -> T1831,\nX3752 -> T1831,\nX3753 -> s(0),\nX3754 -> s(s(s(0))),\nT282 -> s(s(s(0)))" }, { "from": 5062, "to": 5072, "label": "EVAL-BACKTRACK" }, { "from": 5071, "to": 5073, "label": "CASE" }, { "from": 5073, "to": 5074, "label": "PARALLEL" }, { "from": 5073, "to": 5075, "label": "PARALLEL" }, { "from": 5074, "to": 5076, "label": "EVAL with clause\nsmall(0).\nand substitutionT1831 -> 0" }, { "from": 5074, "to": 5077, "label": "EVAL-BACKTRACK" }, { "from": 5075, "to": 5087, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1831 -> s(0)" }, { "from": 5075, "to": 5088, "label": "EVAL-BACKTRACK" }, { "from": 5076, "to": 5078, "label": "CASE" }, { "from": 5078, "to": 5080, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5080, "to": 5083, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5083, "to": 5084, "label": "SUCCESS" }, { "from": 5087, "to": 5089, "label": "CASE" }, { "from": 5089, "to": 5090, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5090, "to": 5091, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5091, "to": 5092, "label": "SUCCESS" }, { "from": 5093, "to": 655, "label": "INSTANCE" }, { "from": 5113, "to": 5115, "label": "CASE" }, { "from": 5115, "to": 5116, "label": "PARALLEL" }, { "from": 5115, "to": 5117, "label": "PARALLEL" }, { "from": 5116, "to": 5118, "label": "EVAL with clause\nsmall(0).\nand substitutionT1838 -> 0" }, { "from": 5116, "to": 5119, "label": "EVAL-BACKTRACK" }, { "from": 5117, "to": 5125, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1838 -> s(0)" }, { "from": 5117, "to": 5126, "label": "EVAL-BACKTRACK" }, { "from": 5118, "to": 5120, "label": "CASE" }, { "from": 5120, "to": 5121, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5121, "to": 5122, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1839 -> 0" }, { "from": 5121, "to": 5123, "label": "EVAL-BACKTRACK" }, { "from": 5122, "to": 5124, "label": "SUCCESS" }, { "from": 5125, "to": 5127, "label": "CASE" }, { "from": 5127, "to": 5128, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5128, "to": 5129, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1839 -> 0" }, { "from": 5128, "to": 5130, "label": "EVAL-BACKTRACK" }, { "from": 5129, "to": 5131, "label": "SUCCESS" }, { "from": 5166, "to": 5189, "label": "ONLY EVAL with clause\nlog2(X3792, s(s(X3793)), X3794, X3795) :- ','(small(X3792), log2(X3793, s(0), s(X3794), X3795)).\nand substitutionT230 -> T1850,\nX3792 -> T1850,\nX3793 -> s(s(s(s(s(0))))),\nX3794 -> s(s(0)),\nT231 -> T1851,\nX3795 -> T1851" }, { "from": 5167, "to": 5207, "label": "EVAL with clause\nlog2(X3814, X3815, X3816, X3816) :- ','(small(X3814), small(X3815)).\nand substitutionT230 -> T1857,\nX3814 -> T1857,\nX3815 -> s(s(s(s(s(s(s(0))))))),\nX3816 -> s(s(0)),\nT231 -> s(s(0))" }, { "from": 5167, "to": 5208, "label": "EVAL-BACKTRACK" }, { "from": 5189, "to": 5191, "label": "CASE" }, { "from": 5191, "to": 5192, "label": "PARALLEL" }, { "from": 5191, "to": 5193, "label": "PARALLEL" }, { "from": 5192, "to": 5194, "label": "EVAL with clause\nsmall(0).\nand substitutionT1850 -> 0" }, { "from": 5192, "to": 5195, "label": "EVAL-BACKTRACK" }, { "from": 5193, "to": 5203, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1850 -> s(0)" }, { "from": 5193, "to": 5204, "label": "EVAL-BACKTRACK" }, { "from": 5194, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(s(s(0)))))\nT282 -> T1851" }, { "from": 5203, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(s(s(0)))))\nT282 -> T1851" }, { "from": 5207, "to": 5209, "label": "CASE" }, { "from": 5209, "to": 5211, "label": "PARALLEL" }, { "from": 5209, "to": 5212, "label": "PARALLEL" }, { "from": 5211, "to": 5213, "label": "EVAL with clause\nsmall(0).\nand substitutionT1857 -> 0" }, { "from": 5211, "to": 5214, "label": "EVAL-BACKTRACK" }, { "from": 5212, "to": 5218, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1857 -> s(0)" }, { "from": 5212, "to": 5219, "label": "EVAL-BACKTRACK" }, { "from": 5213, "to": 5215, "label": "CASE" }, { "from": 5215, "to": 5216, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5216, "to": 5217, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5218, "to": 5220, "label": "CASE" }, { "from": 5220, "to": 5221, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5221, "to": 5222, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5245, "to": 5264, "label": "ONLY EVAL with clause\nlog2(X3841, s(s(X3842)), X3843, X3844) :- ','(small(X3841), log2(X3842, s(0), s(X3843), X3844)).\nand substitutionT218 -> T1868,\nX3841 -> T1868,\nX3842 -> s(s(s(s(0)))),\nX3843 -> s(s(0)),\nT219 -> T1869,\nX3844 -> T1869" }, { "from": 5246, "to": 5284, "label": "EVAL with clause\nlog2(X3863, X3864, X3865, X3865) :- ','(small(X3863), small(X3864)).\nand substitutionT218 -> T1875,\nX3863 -> T1875,\nX3864 -> s(s(s(s(s(s(0)))))),\nX3865 -> s(s(0)),\nT219 -> s(s(0))" }, { "from": 5246, "to": 5287, "label": "EVAL-BACKTRACK" }, { "from": 5264, "to": 5268, "label": "CASE" }, { "from": 5268, "to": 5269, "label": "PARALLEL" }, { "from": 5268, "to": 5270, "label": "PARALLEL" }, { "from": 5269, "to": 5274, "label": "EVAL with clause\nsmall(0).\nand substitutionT1868 -> 0" }, { "from": 5269, "to": 5275, "label": "EVAL-BACKTRACK" }, { "from": 5270, "to": 5278, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1868 -> s(0)" }, { "from": 5270, "to": 5280, "label": "EVAL-BACKTRACK" }, { "from": 5274, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(s(0))))\nT282 -> T1869" }, { "from": 5278, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(s(0))))\nT282 -> T1869" }, { "from": 5284, "to": 5291, "label": "CASE" }, { "from": 5291, "to": 5294, "label": "PARALLEL" }, { "from": 5291, "to": 5295, "label": "PARALLEL" }, { "from": 5294, "to": 5298, "label": "EVAL with clause\nsmall(0).\nand substitutionT1875 -> 0" }, { "from": 5294, "to": 5299, "label": "EVAL-BACKTRACK" }, { "from": 5295, "to": 5308, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1875 -> s(0)" }, { "from": 5295, "to": 5309, "label": "EVAL-BACKTRACK" }, { "from": 5298, "to": 5302, "label": "CASE" }, { "from": 5302, "to": 5303, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5303, "to": 5305, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5308, "to": 5312, "label": "CASE" }, { "from": 5312, "to": 5313, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5313, "to": 5315, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5320, "to": 5339, "label": "ONLY EVAL with clause\nlog2(X3890, s(s(X3891)), X3892, X3893) :- ','(small(X3890), log2(X3891, s(0), s(X3892), X3893)).\nand substitutionT206 -> T1886,\nX3890 -> T1886,\nX3891 -> s(s(s(0))),\nX3892 -> s(s(0)),\nT207 -> T1887,\nX3893 -> T1887" }, { "from": 5321, "to": 5363, "label": "EVAL with clause\nlog2(X3912, X3913, X3914, X3914) :- ','(small(X3912), small(X3913)).\nand substitutionT206 -> T1893,\nX3912 -> T1893,\nX3913 -> s(s(s(s(s(0))))),\nX3914 -> s(s(0)),\nT207 -> s(s(0))" }, { "from": 5321, "to": 5364, "label": "EVAL-BACKTRACK" }, { "from": 5339, "to": 5343, "label": "CASE" }, { "from": 5343, "to": 5344, "label": "PARALLEL" }, { "from": 5343, "to": 5345, "label": "PARALLEL" }, { "from": 5344, "to": 5346, "label": "EVAL with clause\nsmall(0).\nand substitutionT1886 -> 0" }, { "from": 5344, "to": 5347, "label": "EVAL-BACKTRACK" }, { "from": 5345, "to": 5353, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1886 -> s(0)" }, { "from": 5345, "to": 5354, "label": "EVAL-BACKTRACK" }, { "from": 5346, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(0)))\nT282 -> T1887" }, { "from": 5353, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(s(0)))\nT282 -> T1887" }, { "from": 5363, "to": 5365, "label": "CASE" }, { "from": 5365, "to": 5366, "label": "PARALLEL" }, { "from": 5365, "to": 5367, "label": "PARALLEL" }, { "from": 5366, "to": 5368, "label": "EVAL with clause\nsmall(0).\nand substitutionT1893 -> 0" }, { "from": 5366, "to": 5369, "label": "EVAL-BACKTRACK" }, { "from": 5367, "to": 5373, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1893 -> s(0)" }, { "from": 5367, "to": 5374, "label": "EVAL-BACKTRACK" }, { "from": 5368, "to": 5370, "label": "CASE" }, { "from": 5370, "to": 5371, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5371, "to": 5372, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5373, "to": 5376, "label": "CASE" }, { "from": 5376, "to": 5378, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5378, "to": 5379, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5395, "to": 5416, "label": "ONLY EVAL with clause\nlog2(X3939, s(s(X3940)), X3941, X3942) :- ','(small(X3939), log2(X3940, s(0), s(X3941), X3942)).\nand substitutionT194 -> T1904,\nX3939 -> T1904,\nX3940 -> s(s(0)),\nX3941 -> s(s(0)),\nT195 -> T1905,\nX3942 -> T1905" }, { "from": 5396, "to": 5438, "label": "EVAL with clause\nlog2(X3961, X3962, X3963, X3963) :- ','(small(X3961), small(X3962)).\nand substitutionT194 -> T1911,\nX3961 -> T1911,\nX3962 -> s(s(s(s(0)))),\nX3963 -> s(s(0)),\nT195 -> s(s(0))" }, { "from": 5396, "to": 5439, "label": "EVAL-BACKTRACK" }, { "from": 5416, "to": 5418, "label": "CASE" }, { "from": 5418, "to": 5419, "label": "PARALLEL" }, { "from": 5418, "to": 5420, "label": "PARALLEL" }, { "from": 5419, "to": 5422, "label": "EVAL with clause\nsmall(0).\nand substitutionT1904 -> 0" }, { "from": 5419, "to": 5424, "label": "EVAL-BACKTRACK" }, { "from": 5420, "to": 5430, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1904 -> s(0)" }, { "from": 5420, "to": 5431, "label": "EVAL-BACKTRACK" }, { "from": 5422, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(0))\nT282 -> T1905" }, { "from": 5430, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(s(0))\nT282 -> T1905" }, { "from": 5438, "to": 5442, "label": "CASE" }, { "from": 5442, "to": 5443, "label": "PARALLEL" }, { "from": 5442, "to": 5444, "label": "PARALLEL" }, { "from": 5443, "to": 5448, "label": "EVAL with clause\nsmall(0).\nand substitutionT1911 -> 0" }, { "from": 5443, "to": 5449, "label": "EVAL-BACKTRACK" }, { "from": 5444, "to": 5458, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1911 -> s(0)" }, { "from": 5444, "to": 5459, "label": "EVAL-BACKTRACK" }, { "from": 5448, "to": 5451, "label": "CASE" }, { "from": 5451, "to": 5453, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5453, "to": 5454, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5458, "to": 5461, "label": "CASE" }, { "from": 5461, "to": 5463, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5463, "to": 5464, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5470, "to": 5491, "label": "ONLY EVAL with clause\nlog2(X3988, s(s(X3989)), X3990, X3991) :- ','(small(X3988), log2(X3989, s(0), s(X3990), X3991)).\nand substitutionT182 -> T1920,\nX3988 -> T1920,\nX3989 -> s(0),\nX3990 -> s(s(0)),\nT183 -> T1921,\nX3991 -> T1921" }, { "from": 5471, "to": 5513, "label": "EVAL with clause\nlog2(X4010, X4011, X4012, X4012) :- ','(small(X4010), small(X4011)).\nand substitutionT182 -> T1924,\nX4010 -> T1924,\nX4011 -> s(s(s(0))),\nX4012 -> s(s(0)),\nT183 -> s(s(0))" }, { "from": 5471, "to": 5514, "label": "EVAL-BACKTRACK" }, { "from": 5491, "to": 5493, "label": "CASE" }, { "from": 5493, "to": 5494, "label": "PARALLEL" }, { "from": 5493, "to": 5495, "label": "PARALLEL" }, { "from": 5494, "to": 5496, "label": "EVAL with clause\nsmall(0).\nand substitutionT1920 -> 0" }, { "from": 5494, "to": 5497, "label": "EVAL-BACKTRACK" }, { "from": 5495, "to": 5503, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1920 -> s(0)" }, { "from": 5495, "to": 5504, "label": "EVAL-BACKTRACK" }, { "from": 5496, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(0)\nT282 -> T1921" }, { "from": 5503, "to": 655, "label": "INSTANCE with matching:\nT281 -> s(0)\nT282 -> T1921" }, { "from": 5513, "to": 5515, "label": "CASE" }, { "from": 5515, "to": 5516, "label": "PARALLEL" }, { "from": 5515, "to": 5517, "label": "PARALLEL" }, { "from": 5516, "to": 5518, "label": "EVAL with clause\nsmall(0).\nand substitutionT1924 -> 0" }, { "from": 5516, "to": 5519, "label": "EVAL-BACKTRACK" }, { "from": 5517, "to": 5523, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1924 -> s(0)" }, { "from": 5517, "to": 5524, "label": "EVAL-BACKTRACK" }, { "from": 5518, "to": 5520, "label": "CASE" }, { "from": 5520, "to": 5521, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5521, "to": 5522, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5523, "to": 5525, "label": "CASE" }, { "from": 5525, "to": 5526, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5526, "to": 5527, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5546, "to": 5582, "label": "ONLY EVAL with clause\nlog2(X4037, s(s(X4038)), X4039, X4040) :- ','(small(X4037), log2(X4038, s(0), s(X4039), X4040)).\nand substitutionT170 -> T1933,\nX4037 -> T1933,\nX4038 -> 0,\nX4039 -> s(s(0)),\nT171 -> T1934,\nX4040 -> T1934" }, { "from": 5547, "to": 5613, "label": "EVAL with clause\nlog2(X4059, X4060, X4061, X4061) :- ','(small(X4059), small(X4060)).\nand substitutionT170 -> T1937,\nX4059 -> T1937,\nX4060 -> s(s(0)),\nX4061 -> s(s(0)),\nT171 -> s(s(0))" }, { "from": 5547, "to": 5614, "label": "EVAL-BACKTRACK" }, { "from": 5582, "to": 5602, "label": "CASE" }, { "from": 5602, "to": 5603, "label": "PARALLEL" }, { "from": 5602, "to": 5604, "label": "PARALLEL" }, { "from": 5603, "to": 5605, "label": "EVAL with clause\nsmall(0).\nand substitutionT1933 -> 0" }, { "from": 5603, "to": 5606, "label": "EVAL-BACKTRACK" }, { "from": 5604, "to": 5609, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1933 -> s(0)" }, { "from": 5604, "to": 5610, "label": "EVAL-BACKTRACK" }, { "from": 5605, "to": 655, "label": "INSTANCE with matching:\nT281 -> 0\nT282 -> T1934" }, { "from": 5609, "to": 655, "label": "INSTANCE with matching:\nT281 -> 0\nT282 -> T1934" }, { "from": 5613, "to": 5615, "label": "CASE" }, { "from": 5615, "to": 5616, "label": "PARALLEL" }, { "from": 5615, "to": 5617, "label": "PARALLEL" }, { "from": 5616, "to": 5618, "label": "EVAL with clause\nsmall(0).\nand substitutionT1937 -> 0" }, { "from": 5616, "to": 5619, "label": "EVAL-BACKTRACK" }, { "from": 5617, "to": 5624, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1937 -> s(0)" }, { "from": 5617, "to": 5625, "label": "EVAL-BACKTRACK" }, { "from": 5618, "to": 5620, "label": "CASE" }, { "from": 5620, "to": 5621, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5621, "to": 5623, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5624, "to": 5626, "label": "CASE" }, { "from": 5626, "to": 5627, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5627, "to": 5628, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5635, "to": 5645, "label": "EVAL with clause\nlog2(X4072, X4073, X4074, X4074) :- ','(small(X4072), small(X4073)).\nand substitutionT155 -> T1941,\nX4072 -> T1941,\nX4073 -> s(0),\nX4074 -> s(s(0)),\nT156 -> s(s(0))" }, { "from": 5635, "to": 5646, "label": "EVAL-BACKTRACK" }, { "from": 5645, "to": 5647, "label": "CASE" }, { "from": 5647, "to": 5648, "label": "PARALLEL" }, { "from": 5647, "to": 5649, "label": "PARALLEL" }, { "from": 5648, "to": 5650, "label": "EVAL with clause\nsmall(0).\nand substitutionT1941 -> 0" }, { "from": 5648, "to": 5651, "label": "EVAL-BACKTRACK" }, { "from": 5649, "to": 5656, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1941 -> s(0)" }, { "from": 5649, "to": 5657, "label": "EVAL-BACKTRACK" }, { "from": 5650, "to": 5652, "label": "CASE" }, { "from": 5652, "to": 5653, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5653, "to": 5654, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5654, "to": 5655, "label": "SUCCESS" }, { "from": 5656, "to": 5658, "label": "CASE" }, { "from": 5658, "to": 5659, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5659, "to": 5660, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5660, "to": 5661, "label": "SUCCESS" }, { "from": 5662, "to": 487, "label": "INSTANCE" }, { "from": 5695, "to": 5697, "label": "CASE" }, { "from": 5697, "to": 5698, "label": "PARALLEL" }, { "from": 5697, "to": 5699, "label": "PARALLEL" }, { "from": 5698, "to": 5700, "label": "EVAL with clause\nsmall(0).\nand substitutionT1950 -> 0" }, { "from": 5698, "to": 5701, "label": "EVAL-BACKTRACK" }, { "from": 5699, "to": 5707, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1950 -> s(0)" }, { "from": 5699, "to": 5708, "label": "EVAL-BACKTRACK" }, { "from": 5700, "to": 5702, "label": "CASE" }, { "from": 5702, "to": 5703, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5703, "to": 5704, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1949 -> 0" }, { "from": 5703, "to": 5705, "label": "EVAL-BACKTRACK" }, { "from": 5704, "to": 5706, "label": "SUCCESS" }, { "from": 5707, "to": 5711, "label": "CASE" }, { "from": 5711, "to": 5712, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5712, "to": 5713, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1949 -> 0" }, { "from": 5712, "to": 5714, "label": "EVAL-BACKTRACK" }, { "from": 5713, "to": 5715, "label": "SUCCESS" }, { "from": 5735, "to": 5764, "label": "ONLY EVAL with clause\nlog2(X4112, s(s(X4113)), X4114, X4115) :- ','(small(X4112), log2(X4113, s(0), s(X4114), X4115)).\nand substitutionT103 -> T1965,\nX4112 -> T1965,\nX4113 -> s(s(s(s(s(0))))),\nX4114 -> s(0),\nT102 -> T1964,\nX4115 -> T1964,\nT1963 -> T1965" }, { "from": 5736, "to": 5792, "label": "EVAL with clause\nlog2(X4134, X4135, X4136, X4136) :- ','(small(X4134), small(X4135)).\nand substitutionT103 -> T1972,\nX4134 -> T1972,\nX4135 -> s(s(s(s(s(s(s(0))))))),\nX4136 -> s(0),\nT102 -> s(0),\nT1971 -> T1972" }, { "from": 5736, "to": 5793, "label": "EVAL-BACKTRACK" }, { "from": 5764, "to": 5767, "label": "CASE" }, { "from": 5767, "to": 5768, "label": "PARALLEL" }, { "from": 5767, "to": 5769, "label": "PARALLEL" }, { "from": 5768, "to": 5770, "label": "EVAL with clause\nsmall(0).\nand substitutionT1965 -> 0" }, { "from": 5768, "to": 5771, "label": "EVAL-BACKTRACK" }, { "from": 5769, "to": 5774, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1965 -> s(0)" }, { "from": 5769, "to": 5775, "label": "EVAL-BACKTRACK" }, { "from": 5770, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(s(s(0)))))\nT156 -> T1964" }, { "from": 5774, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(s(s(0)))))\nT156 -> T1964" }, { "from": 5792, "to": 5794, "label": "CASE" }, { "from": 5794, "to": 5795, "label": "PARALLEL" }, { "from": 5794, "to": 5796, "label": "PARALLEL" }, { "from": 5795, "to": 5797, "label": "EVAL with clause\nsmall(0).\nand substitutionT1972 -> 0" }, { "from": 5795, "to": 5798, "label": "EVAL-BACKTRACK" }, { "from": 5796, "to": 5802, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1972 -> s(0)" }, { "from": 5796, "to": 5803, "label": "EVAL-BACKTRACK" }, { "from": 5797, "to": 5799, "label": "CASE" }, { "from": 5799, "to": 5800, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5800, "to": 5801, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5802, "to": 5804, "label": "CASE" }, { "from": 5804, "to": 5805, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5805, "to": 5806, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5814, "to": 5841, "label": "ONLY EVAL with clause\nlog2(X4161, s(s(X4162)), X4163, X4164) :- ','(small(X4161), log2(X4162, s(0), s(X4163), X4164)).\nand substitutionT90 -> T1987,\nX4161 -> T1987,\nX4162 -> s(s(s(s(0)))),\nX4163 -> s(0),\nT89 -> T1986,\nX4164 -> T1986,\nT1985 -> T1987" }, { "from": 5815, "to": 5872, "label": "EVAL with clause\nlog2(X4183, X4184, X4185, X4185) :- ','(small(X4183), small(X4184)).\nand substitutionT90 -> T1994,\nX4183 -> T1994,\nX4184 -> s(s(s(s(s(s(0)))))),\nX4185 -> s(0),\nT89 -> s(0),\nT1993 -> T1994" }, { "from": 5815, "to": 5873, "label": "EVAL-BACKTRACK" }, { "from": 5841, "to": 5843, "label": "CASE" }, { "from": 5843, "to": 5845, "label": "PARALLEL" }, { "from": 5843, "to": 5846, "label": "PARALLEL" }, { "from": 5845, "to": 5849, "label": "EVAL with clause\nsmall(0).\nand substitutionT1987 -> 0" }, { "from": 5845, "to": 5851, "label": "EVAL-BACKTRACK" }, { "from": 5846, "to": 5862, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1987 -> s(0)" }, { "from": 5846, "to": 5863, "label": "EVAL-BACKTRACK" }, { "from": 5849, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(s(0))))\nT156 -> T1986" }, { "from": 5862, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(s(0))))\nT156 -> T1986" }, { "from": 5872, "to": 5874, "label": "CASE" }, { "from": 5874, "to": 5875, "label": "PARALLEL" }, { "from": 5874, "to": 5876, "label": "PARALLEL" }, { "from": 5875, "to": 5877, "label": "EVAL with clause\nsmall(0).\nand substitutionT1994 -> 0" }, { "from": 5875, "to": 5878, "label": "EVAL-BACKTRACK" }, { "from": 5876, "to": 5882, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1994 -> s(0)" }, { "from": 5876, "to": 5883, "label": "EVAL-BACKTRACK" }, { "from": 5877, "to": 5879, "label": "CASE" }, { "from": 5879, "to": 5880, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5880, "to": 5881, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5882, "to": 5884, "label": "CASE" }, { "from": 5884, "to": 5885, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5885, "to": 5886, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5889, "to": 5912, "label": "ONLY EVAL with clause\nlog2(X4210, s(s(X4211)), X4212, X4213) :- ','(small(X4210), log2(X4211, s(0), s(X4212), X4213)).\nand substitutionT77 -> T2009,\nX4210 -> T2009,\nX4211 -> s(s(s(0))),\nX4212 -> s(0),\nT76 -> T2008,\nX4213 -> T2008,\nT2007 -> T2009" }, { "from": 5890, "to": 5924, "label": "EVAL with clause\nlog2(X4232, X4233, X4234, X4234) :- ','(small(X4232), small(X4233)).\nand substitutionT77 -> T2016,\nX4232 -> T2016,\nX4233 -> s(s(s(s(s(0))))),\nX4234 -> s(0),\nT76 -> s(0),\nT2015 -> T2016" }, { "from": 5890, "to": 5925, "label": "EVAL-BACKTRACK" }, { "from": 5912, "to": 5913, "label": "CASE" }, { "from": 5913, "to": 5916, "label": "PARALLEL" }, { "from": 5913, "to": 5917, "label": "PARALLEL" }, { "from": 5916, "to": 5918, "label": "EVAL with clause\nsmall(0).\nand substitutionT2009 -> 0" }, { "from": 5916, "to": 5919, "label": "EVAL-BACKTRACK" }, { "from": 5917, "to": 5920, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2009 -> s(0)" }, { "from": 5917, "to": 5921, "label": "EVAL-BACKTRACK" }, { "from": 5918, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(0)))\nT156 -> T2008" }, { "from": 5920, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(s(0)))\nT156 -> T2008" }, { "from": 5924, "to": 5926, "label": "CASE" }, { "from": 5926, "to": 5927, "label": "PARALLEL" }, { "from": 5926, "to": 5928, "label": "PARALLEL" }, { "from": 5927, "to": 5929, "label": "EVAL with clause\nsmall(0).\nand substitutionT2016 -> 0" }, { "from": 5927, "to": 5930, "label": "EVAL-BACKTRACK" }, { "from": 5928, "to": 5934, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2016 -> s(0)" }, { "from": 5928, "to": 5935, "label": "EVAL-BACKTRACK" }, { "from": 5929, "to": 5931, "label": "CASE" }, { "from": 5931, "to": 5932, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5932, "to": 5933, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5934, "to": 5936, "label": "CASE" }, { "from": 5936, "to": 5937, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5937, "to": 5938, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5955, "to": 5966, "label": "ONLY EVAL with clause\nlog2(X4259, s(s(X4260)), X4261, X4262) :- ','(small(X4259), log2(X4260, s(0), s(X4261), X4262)).\nand substitutionT64 -> T2031,\nX4259 -> T2031,\nX4260 -> s(s(0)),\nX4261 -> s(0),\nT63 -> T2030,\nX4262 -> T2030,\nT2029 -> T2031" }, { "from": 5956, "to": 5999, "label": "EVAL with clause\nlog2(X4281, X4282, X4283, X4283) :- ','(small(X4281), small(X4282)).\nand substitutionT64 -> T2038,\nX4281 -> T2038,\nX4282 -> s(s(s(s(0)))),\nX4283 -> s(0),\nT63 -> s(0),\nT2037 -> T2038" }, { "from": 5956, "to": 6000, "label": "EVAL-BACKTRACK" }, { "from": 5966, "to": 5983, "label": "CASE" }, { "from": 5983, "to": 5984, "label": "PARALLEL" }, { "from": 5983, "to": 5985, "label": "PARALLEL" }, { "from": 5984, "to": 5986, "label": "EVAL with clause\nsmall(0).\nand substitutionT2031 -> 0" }, { "from": 5984, "to": 5987, "label": "EVAL-BACKTRACK" }, { "from": 5985, "to": 5993, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2031 -> s(0)" }, { "from": 5985, "to": 5994, "label": "EVAL-BACKTRACK" }, { "from": 5986, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(0))\nT156 -> T2030" }, { "from": 5993, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(s(0))\nT156 -> T2030" }, { "from": 5999, "to": 6001, "label": "CASE" }, { "from": 6001, "to": 6002, "label": "PARALLEL" }, { "from": 6001, "to": 6003, "label": "PARALLEL" }, { "from": 6002, "to": 6004, "label": "EVAL with clause\nsmall(0).\nand substitutionT2038 -> 0" }, { "from": 6002, "to": 6005, "label": "EVAL-BACKTRACK" }, { "from": 6003, "to": 6009, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2038 -> s(0)" }, { "from": 6003, "to": 6010, "label": "EVAL-BACKTRACK" }, { "from": 6004, "to": 6006, "label": "CASE" }, { "from": 6006, "to": 6007, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6007, "to": 6008, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6009, "to": 6011, "label": "CASE" }, { "from": 6011, "to": 6012, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6012, "to": 6013, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6035, "to": 6041, "label": "ONLY EVAL with clause\nlog2(X4308, s(s(X4309)), X4310, X4311) :- ','(small(X4308), log2(X4309, s(0), s(X4310), X4311)).\nand substitutionT51 -> T2051,\nX4308 -> T2051,\nX4309 -> s(0),\nX4310 -> s(0),\nT50 -> T2050,\nX4311 -> T2050,\nT2049 -> T2051" }, { "from": 6036, "to": 6074, "label": "EVAL with clause\nlog2(X4330, X4331, X4332, X4332) :- ','(small(X4330), small(X4331)).\nand substitutionT51 -> T2055,\nX4330 -> T2055,\nX4331 -> s(s(s(0))),\nX4332 -> s(0),\nT50 -> s(0),\nT2054 -> T2055" }, { "from": 6036, "to": 6075, "label": "EVAL-BACKTRACK" }, { "from": 6041, "to": 6058, "label": "CASE" }, { "from": 6058, "to": 6059, "label": "PARALLEL" }, { "from": 6058, "to": 6060, "label": "PARALLEL" }, { "from": 6059, "to": 6061, "label": "EVAL with clause\nsmall(0).\nand substitutionT2051 -> 0" }, { "from": 6059, "to": 6062, "label": "EVAL-BACKTRACK" }, { "from": 6060, "to": 6068, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2051 -> s(0)" }, { "from": 6060, "to": 6069, "label": "EVAL-BACKTRACK" }, { "from": 6061, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(0)\nT156 -> T2050" }, { "from": 6068, "to": 487, "label": "INSTANCE with matching:\nT155 -> s(0)\nT156 -> T2050" }, { "from": 6074, "to": 6076, "label": "CASE" }, { "from": 6076, "to": 6077, "label": "PARALLEL" }, { "from": 6076, "to": 6078, "label": "PARALLEL" }, { "from": 6077, "to": 6079, "label": "EVAL with clause\nsmall(0).\nand substitutionT2055 -> 0" }, { "from": 6077, "to": 6080, "label": "EVAL-BACKTRACK" }, { "from": 6078, "to": 6084, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2055 -> s(0)" }, { "from": 6078, "to": 6085, "label": "EVAL-BACKTRACK" }, { "from": 6079, "to": 6081, "label": "CASE" }, { "from": 6081, "to": 6082, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6082, "to": 6083, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6084, "to": 6086, "label": "CASE" }, { "from": 6086, "to": 6087, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6087, "to": 6088, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6111, "to": 6148, "label": "ONLY EVAL with clause\nlog2(X4357, s(s(X4358)), X4359, X4360) :- ','(small(X4357), log2(X4358, s(0), s(X4359), X4360)).\nand substitutionT38 -> T2068,\nX4357 -> T2068,\nX4358 -> 0,\nX4359 -> s(0),\nT37 -> T2067,\nX4360 -> T2067,\nT2066 -> T2068" }, { "from": 6112, "to": 6179, "label": "EVAL with clause\nlog2(X4379, X4380, X4381, X4381) :- ','(small(X4379), small(X4380)).\nand substitutionT38 -> T2072,\nX4379 -> T2072,\nX4380 -> s(s(0)),\nX4381 -> s(0),\nT37 -> s(0),\nT2071 -> T2072" }, { "from": 6112, "to": 6180, "label": "EVAL-BACKTRACK" }, { "from": 6148, "to": 6165, "label": "CASE" }, { "from": 6165, "to": 6168, "label": "PARALLEL" }, { "from": 6165, "to": 6169, "label": "PARALLEL" }, { "from": 6168, "to": 6173, "label": "EVAL with clause\nsmall(0).\nand substitutionT2068 -> 0" }, { "from": 6168, "to": 6174, "label": "EVAL-BACKTRACK" }, { "from": 6169, "to": 6175, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2068 -> s(0)" }, { "from": 6169, "to": 6176, "label": "EVAL-BACKTRACK" }, { "from": 6173, "to": 487, "label": "INSTANCE with matching:\nT155 -> 0\nT156 -> T2067" }, { "from": 6175, "to": 487, "label": "INSTANCE with matching:\nT155 -> 0\nT156 -> T2067" }, { "from": 6179, "to": 6181, "label": "CASE" }, { "from": 6181, "to": 6182, "label": "PARALLEL" }, { "from": 6181, "to": 6183, "label": "PARALLEL" }, { "from": 6182, "to": 6184, "label": "EVAL with clause\nsmall(0).\nand substitutionT2072 -> 0" }, { "from": 6182, "to": 6185, "label": "EVAL-BACKTRACK" }, { "from": 6183, "to": 6189, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2072 -> s(0)" }, { "from": 6183, "to": 6190, "label": "EVAL-BACKTRACK" }, { "from": 6184, "to": 6186, "label": "CASE" }, { "from": 6186, "to": 6187, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6187, "to": 6188, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6189, "to": 6191, "label": "CASE" }, { "from": 6191, "to": 6192, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6192, "to": 6193, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6194, "to": 6201, "label": "EVAL with clause\nlog2(X4392, X4393, X4394, X4394) :- ','(small(X4392), small(X4393)).\nand substitutionT25 -> T2077,\nX4392 -> T2077,\nX4393 -> s(0),\nX4394 -> s(0),\nT24 -> s(0),\nT2076 -> T2077" }, { "from": 6194, "to": 6202, "label": "EVAL-BACKTRACK" }, { "from": 6201, "to": 6203, "label": "CASE" }, { "from": 6203, "to": 6204, "label": "PARALLEL" }, { "from": 6203, "to": 6205, "label": "PARALLEL" }, { "from": 6204, "to": 6206, "label": "EVAL with clause\nsmall(0).\nand substitutionT2077 -> 0" }, { "from": 6204, "to": 6208, "label": "EVAL-BACKTRACK" }, { "from": 6205, "to": 6214, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2077 -> s(0)" }, { "from": 6205, "to": 6215, "label": "EVAL-BACKTRACK" }, { "from": 6206, "to": 6210, "label": "CASE" }, { "from": 6210, "to": 6211, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6211, "to": 6212, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 6212, "to": 6213, "label": "SUCCESS" }, { "from": 6214, "to": 6216, "label": "CASE" }, { "from": 6216, "to": 6217, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6217, "to": 6218, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 6218, "to": 6219, "label": "SUCCESS" }, { "from": 6220, "to": 6236, "label": "EVAL with clause\nlog2(X4405, X4406, X4407, X4407) :- ','(small(X4405), small(X4406)).\nand substitutionT12 -> T2082,\nX4405 -> T2082,\nX4406 -> 0,\nX4407 -> s(0),\nT11 -> s(0),\nT2081 -> T2082" }, { "from": 6220, "to": 6237, "label": "EVAL-BACKTRACK" }, { "from": 6236, "to": 6238, "label": "CASE" }, { "from": 6238, "to": 6239, "label": "PARALLEL" }, { "from": 6238, "to": 6240, "label": "PARALLEL" }, { "from": 6239, "to": 6241, "label": "EVAL with clause\nsmall(0).\nand substitutionT2082 -> 0" }, { "from": 6239, "to": 6242, "label": "EVAL-BACKTRACK" }, { "from": 6240, "to": 6249, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2082 -> s(0)" }, { "from": 6240, "to": 6250, "label": "EVAL-BACKTRACK" }, { "from": 6241, "to": 6243, "label": "CASE" }, { "from": 6243, "to": 6244, "label": "PARALLEL" }, { "from": 6243, "to": 6245, "label": "PARALLEL" }, { "from": 6244, "to": 6246, "label": "ONLY EVAL with clause\nsmall(0).\nand substitution" }, { "from": 6245, "to": 6248, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6246, "to": 6247, "label": "SUCCESS" }, { "from": 6249, "to": 6251, "label": "CASE" }, { "from": 6251, "to": 6252, "label": "PARALLEL" }, { "from": 6251, "to": 6253, "label": "PARALLEL" }, { "from": 6252, "to": 6254, "label": "ONLY EVAL with clause\nsmall(0).\nand substitution" }, { "from": 6253, "to": 6256, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6254, "to": 6255, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (54) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. ---------------------------------------- (55) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (56) Obligation: Q DP problem: The TRS P consists of the following rules: F3_IN(T115) -> U1^1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) F3_IN(T115) -> F430_IN(s(s(s(s(s(s(s(0))))))), T115) F3_IN(T1964) -> U2^1(f487_in(s(s(s(s(s(0))))), T1964), T1964) F3_IN(T1964) -> F487_IN(s(s(s(s(s(0))))), T1964) F3_IN(T1964) -> U3^1(f487_in(s(s(s(s(s(0))))), T1964), T1964) F3_IN(T1986) -> U4^1(f487_in(s(s(s(s(0)))), T1986), T1986) F3_IN(T1986) -> F487_IN(s(s(s(s(0)))), T1986) F3_IN(T1986) -> U5^1(f487_in(s(s(s(s(0)))), T1986), T1986) F3_IN(T2008) -> U6^1(f487_in(s(s(s(0))), T2008), T2008) F3_IN(T2008) -> F487_IN(s(s(s(0))), T2008) F3_IN(T2008) -> U7^1(f487_in(s(s(s(0))), T2008), T2008) F3_IN(T2030) -> U8^1(f487_in(s(s(0)), T2030), T2030) F3_IN(T2030) -> F487_IN(s(s(0)), T2030) F3_IN(T2030) -> U9^1(f487_in(s(s(0)), T2030), T2030) F3_IN(T2050) -> U10^1(f487_in(s(0), T2050), T2050) F3_IN(T2050) -> F487_IN(s(0), T2050) F3_IN(T2050) -> U11^1(f487_in(s(0), T2050), T2050) F3_IN(T2067) -> U12^1(f487_in(0, T2067), T2067) F3_IN(T2067) -> F487_IN(0, T2067) F3_IN(T2067) -> U13^1(f487_in(0, T2067), T2067) F430_IN(T136, T137) -> U14^1(f430_in(s(T136), T137), T136, T137) F430_IN(T136, T137) -> F430_IN(s(T136), T137) F430_IN(s(T155), T156) -> U15^1(f487_in(T155, T156), s(T155), T156) F430_IN(s(T155), T156) -> F487_IN(T155, T156) F430_IN(s(T155), T156) -> U16^1(f487_in(T155, T156), s(T155), T156) F589_IN(s(s(T262)), T263, T264) -> U17^1(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) F589_IN(s(s(T262)), T263, T264) -> F589_IN(T262, s(T263), T264) F589_IN(0, s(T281), T282) -> U18^1(f655_in(T281, T282), 0, s(T281), T282) F589_IN(0, s(T281), T282) -> F655_IN(T281, T282) F589_IN(s(0), s(T281), T282) -> U19^1(f655_in(T281, T282), s(0), s(T281), T282) F589_IN(s(0), s(T281), T282) -> F655_IN(T281, T282) F752_IN(s(s(T387)), T388, T389) -> U20^1(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) F752_IN(s(s(T387)), T388, T389) -> F752_IN(T387, s(T388), T389) F752_IN(0, s(T406), T407) -> U21^1(f786_in(T406, T407), 0, s(T406), T407) F752_IN(0, s(T406), T407) -> F786_IN(T406, T407) F752_IN(s(0), s(T406), T407) -> U22^1(f786_in(T406, T407), s(0), s(T406), T407) F752_IN(s(0), s(T406), T407) -> F786_IN(T406, T407) F902_IN(s(s(T512)), T513, T514) -> U23^1(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) F902_IN(s(s(T512)), T513, T514) -> F902_IN(T512, s(T513), T514) F902_IN(0, s(T531), T532) -> U24^1(f931_in(T531, T532), 0, s(T531), T532) F902_IN(0, s(T531), T532) -> F931_IN(T531, T532) F902_IN(s(0), s(T531), T532) -> U25^1(f931_in(T531, T532), s(0), s(T531), T532) F902_IN(s(0), s(T531), T532) -> F931_IN(T531, T532) F1045_IN(s(s(T637)), T638, T639) -> U26^1(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) F1045_IN(s(s(T637)), T638, T639) -> F1045_IN(T637, s(T638), T639) F1045_IN(0, s(T656), T657) -> U27^1(f1094_in(T656, T657), 0, s(T656), T657) F1045_IN(0, s(T656), T657) -> F1094_IN(T656, T657) F1045_IN(s(0), s(T656), T657) -> U28^1(f1094_in(T656, T657), s(0), s(T656), T657) F1045_IN(s(0), s(T656), T657) -> F1094_IN(T656, T657) F1241_IN(s(s(T762)), T763, T764) -> U29^1(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) F1241_IN(s(s(T762)), T763, T764) -> F1241_IN(T762, s(T763), T764) F1241_IN(0, s(T781), T782) -> U30^1(f1286_in(T781, T782), 0, s(T781), T782) F1241_IN(0, s(T781), T782) -> F1286_IN(T781, T782) F1241_IN(s(0), s(T781), T782) -> U31^1(f1286_in(T781, T782), s(0), s(T781), T782) F1241_IN(s(0), s(T781), T782) -> F1286_IN(T781, T782) F1416_IN(s(s(T887)), T888, T889) -> U32^1(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) F1416_IN(s(s(T887)), T888, T889) -> F1416_IN(T887, s(T888), T889) F1416_IN(0, s(T906), T907) -> U33^1(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) F1416_IN(0, s(T906), T907) -> F1442_IN(T906, s(s(s(s(s(s(s(0))))))), T907) F1416_IN(s(0), s(T906), T907) -> U34^1(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) F1416_IN(s(0), s(T906), T907) -> F1442_IN(T906, s(s(s(s(s(s(s(0))))))), T907) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35^1(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> F1608_IN(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36^1(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> F1442_IN(s(s(s(s(s(0))))), s(T1126), T1127) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37^1(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> F1442_IN(s(s(s(s(s(0))))), s(T1126), T1127) F1442_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38^1(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) F1442_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> F1442_IN(s(s(s(s(0)))), s(T1157), T1158) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39^1(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) F1442_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> F1442_IN(s(s(s(s(0)))), s(T1157), T1158) F1442_IN(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40^1(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) F1442_IN(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> F1442_IN(s(s(s(0))), s(T1188), T1189) F1442_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41^1(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) F1442_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> F1442_IN(s(s(s(0))), s(T1188), T1189) F1442_IN(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42^1(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) F1442_IN(s(s(s(s(s(s(0)))))), T1219, T1220) -> F1442_IN(s(s(0)), s(T1219), T1220) F1442_IN(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43^1(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) F1442_IN(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> F1442_IN(s(s(0)), s(T1219), T1220) F1442_IN(s(s(s(s(0)))), T1246, T1247) -> U44^1(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) F1442_IN(s(s(s(s(0)))), T1246, T1247) -> F1442_IN(s(0), s(T1246), T1247) F1442_IN(s(s(s(s(s(0))))), T1246, T1247) -> U45^1(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) F1442_IN(s(s(s(s(s(0))))), T1246, T1247) -> F1442_IN(s(0), s(T1246), T1247) F1442_IN(s(s(0)), T1267, T1268) -> U46^1(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) F1442_IN(s(s(0)), T1267, T1268) -> F1442_IN(0, s(T1267), T1268) F1442_IN(s(s(s(0))), T1267, T1268) -> U47^1(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) F1442_IN(s(s(s(0))), T1267, T1268) -> F1442_IN(0, s(T1267), T1268) F1608_IN(s(s(T1063)), T1064, T1065, T1066) -> U48^1(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) F1608_IN(s(s(T1063)), T1064, T1065, T1066) -> F1608_IN(T1063, s(T1064), T1065, T1066) F1608_IN(0, s(T1088), T1089, T1090) -> U49^1(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) F1608_IN(0, s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) F1608_IN(s(0), s(T1088), T1089, T1090) -> U50^1(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) F1608_IN(s(0), s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51^1(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> F1416_IN(T867, s(s(s(s(s(s(s(0))))))), T868) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52^1(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> F1442_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53^1(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> F1442_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301) F1286_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54^1(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) F1286_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> F1442_IN(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55^1(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) F1286_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> F1442_IN(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319) F1286_IN(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56^1(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) F1286_IN(s(s(s(s(s(s(s(s(0)))))))), T1337) -> F1442_IN(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337) F1286_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57^1(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) F1286_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> F1442_IN(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337) F1286_IN(s(s(s(s(s(s(0)))))), T1355) -> U58^1(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) F1286_IN(s(s(s(s(s(s(0)))))), T1355) -> F1442_IN(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355) F1286_IN(s(s(s(s(s(s(s(0))))))), T1355) -> U59^1(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) F1286_IN(s(s(s(s(s(s(s(0))))))), T1355) -> F1442_IN(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355) F1286_IN(s(s(s(s(0)))), T1371) -> U60^1(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) F1286_IN(s(s(s(s(0)))), T1371) -> F1442_IN(s(0), s(s(s(s(s(s(s(0))))))), T1371) F1286_IN(s(s(s(s(s(0))))), T1371) -> U61^1(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) F1286_IN(s(s(s(s(s(0))))), T1371) -> F1442_IN(s(0), s(s(s(s(s(s(s(0))))))), T1371) F1286_IN(s(s(0)), T1384) -> U62^1(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) F1286_IN(s(s(0)), T1384) -> F1442_IN(0, s(s(s(s(s(s(s(0))))))), T1384) F1286_IN(s(s(s(0))), T1384) -> U63^1(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) F1286_IN(s(s(s(0))), T1384) -> F1442_IN(0, s(s(s(s(s(s(s(0))))))), T1384) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64^1(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> F1241_IN(T742, s(s(s(s(s(s(s(0))))))), T743) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65^1(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> F1286_IN(s(s(s(s(s(0))))), T1411) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66^1(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> F1286_IN(s(s(s(s(s(0))))), T1411) F1094_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67^1(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) F1094_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> F1286_IN(s(s(s(s(0)))), T1429) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68^1(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) F1094_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> F1286_IN(s(s(s(s(0)))), T1429) F1094_IN(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69^1(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) F1094_IN(s(s(s(s(s(s(s(s(0)))))))), T1447) -> F1286_IN(s(s(s(0))), T1447) F1094_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70^1(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) F1094_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> F1286_IN(s(s(s(0))), T1447) F1094_IN(s(s(s(s(s(s(0)))))), T1465) -> U71^1(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) F1094_IN(s(s(s(s(s(s(0)))))), T1465) -> F1286_IN(s(s(0)), T1465) F1094_IN(s(s(s(s(s(s(s(0))))))), T1465) -> U72^1(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) F1094_IN(s(s(s(s(s(s(s(0))))))), T1465) -> F1286_IN(s(s(0)), T1465) F1094_IN(s(s(s(s(0)))), T1481) -> U73^1(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) F1094_IN(s(s(s(s(0)))), T1481) -> F1286_IN(s(0), T1481) F1094_IN(s(s(s(s(s(0))))), T1481) -> U74^1(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) F1094_IN(s(s(s(s(s(0))))), T1481) -> F1286_IN(s(0), T1481) F1094_IN(s(s(0)), T1494) -> U75^1(f1286_in(0, T1494), s(s(0)), T1494) F1094_IN(s(s(0)), T1494) -> F1286_IN(0, T1494) F1094_IN(s(s(s(0))), T1494) -> U76^1(f1286_in(0, T1494), s(s(s(0))), T1494) F1094_IN(s(s(s(0))), T1494) -> F1286_IN(0, T1494) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77^1(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> F1045_IN(T617, s(s(s(s(s(s(s(0))))))), T618) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78^1(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> F1094_IN(s(s(s(s(s(0))))), T1521) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79^1(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) F931_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> F1094_IN(s(s(s(s(s(0))))), T1521) F931_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80^1(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) F931_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> F1094_IN(s(s(s(s(0)))), T1539) F931_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81^1(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) F931_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> F1094_IN(s(s(s(s(0)))), T1539) F931_IN(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82^1(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) F931_IN(s(s(s(s(s(s(s(s(0)))))))), T1557) -> F1094_IN(s(s(s(0))), T1557) F931_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83^1(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) F931_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> F1094_IN(s(s(s(0))), T1557) F931_IN(s(s(s(s(s(s(0)))))), T1575) -> U84^1(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) F931_IN(s(s(s(s(s(s(0)))))), T1575) -> F1094_IN(s(s(0)), T1575) F931_IN(s(s(s(s(s(s(s(0))))))), T1575) -> U85^1(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) F931_IN(s(s(s(s(s(s(s(0))))))), T1575) -> F1094_IN(s(s(0)), T1575) F931_IN(s(s(s(s(0)))), T1591) -> U86^1(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) F931_IN(s(s(s(s(0)))), T1591) -> F1094_IN(s(0), T1591) F931_IN(s(s(s(s(s(0))))), T1591) -> U87^1(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) F931_IN(s(s(s(s(s(0))))), T1591) -> F1094_IN(s(0), T1591) F931_IN(s(s(0)), T1604) -> U88^1(f1094_in(0, T1604), s(s(0)), T1604) F931_IN(s(s(0)), T1604) -> F1094_IN(0, T1604) F931_IN(s(s(s(0))), T1604) -> U89^1(f1094_in(0, T1604), s(s(s(0))), T1604) F931_IN(s(s(s(0))), T1604) -> F1094_IN(0, T1604) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90^1(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> F902_IN(T492, s(s(s(s(s(s(s(0))))))), T493) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91^1(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> F931_IN(s(s(s(s(s(0))))), T1631) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92^1(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) F786_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> F931_IN(s(s(s(s(s(0))))), T1631) F786_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93^1(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) F786_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> F931_IN(s(s(s(s(0)))), T1649) F786_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94^1(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) F786_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> F931_IN(s(s(s(s(0)))), T1649) F786_IN(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95^1(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) F786_IN(s(s(s(s(s(s(s(s(0)))))))), T1667) -> F931_IN(s(s(s(0))), T1667) F786_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96^1(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) F786_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> F931_IN(s(s(s(0))), T1667) F786_IN(s(s(s(s(s(s(0)))))), T1685) -> U97^1(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) F786_IN(s(s(s(s(s(s(0)))))), T1685) -> F931_IN(s(s(0)), T1685) F786_IN(s(s(s(s(s(s(s(0))))))), T1685) -> U98^1(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) F786_IN(s(s(s(s(s(s(s(0))))))), T1685) -> F931_IN(s(s(0)), T1685) F786_IN(s(s(s(s(0)))), T1701) -> U99^1(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) F786_IN(s(s(s(s(0)))), T1701) -> F931_IN(s(0), T1701) F786_IN(s(s(s(s(s(0))))), T1701) -> U100^1(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) F786_IN(s(s(s(s(s(0))))), T1701) -> F931_IN(s(0), T1701) F786_IN(s(s(0)), T1714) -> U101^1(f931_in(0, T1714), s(s(0)), T1714) F786_IN(s(s(0)), T1714) -> F931_IN(0, T1714) F786_IN(s(s(s(0))), T1714) -> U102^1(f931_in(0, T1714), s(s(s(0))), T1714) F786_IN(s(s(s(0))), T1714) -> F931_IN(0, T1714) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103^1(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> F752_IN(T367, s(s(s(s(s(s(s(0))))))), T368) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104^1(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> F786_IN(s(s(s(s(s(0))))), T1741) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105^1(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) F655_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> F786_IN(s(s(s(s(s(0))))), T1741) F655_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106^1(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) F655_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> F786_IN(s(s(s(s(0)))), T1759) F655_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107^1(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) F655_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> F786_IN(s(s(s(s(0)))), T1759) F655_IN(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108^1(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) F655_IN(s(s(s(s(s(s(s(s(0)))))))), T1777) -> F786_IN(s(s(s(0))), T1777) F655_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109^1(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) F655_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> F786_IN(s(s(s(0))), T1777) F655_IN(s(s(s(s(s(s(0)))))), T1795) -> U110^1(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) F655_IN(s(s(s(s(s(s(0)))))), T1795) -> F786_IN(s(s(0)), T1795) F655_IN(s(s(s(s(s(s(s(0))))))), T1795) -> U111^1(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) F655_IN(s(s(s(s(s(s(s(0))))))), T1795) -> F786_IN(s(s(0)), T1795) F655_IN(s(s(s(s(0)))), T1811) -> U112^1(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) F655_IN(s(s(s(s(0)))), T1811) -> F786_IN(s(0), T1811) F655_IN(s(s(s(s(s(0))))), T1811) -> U113^1(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) F655_IN(s(s(s(s(s(0))))), T1811) -> F786_IN(s(0), T1811) F655_IN(s(s(0)), T1824) -> U114^1(f786_in(0, T1824), s(s(0)), T1824) F655_IN(s(s(0)), T1824) -> F786_IN(0, T1824) F655_IN(s(s(s(0))), T1824) -> U115^1(f786_in(0, T1824), s(s(s(0))), T1824) F655_IN(s(s(s(0))), T1824) -> F786_IN(0, T1824) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116^1(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> F589_IN(T242, s(s(s(s(s(s(s(0))))))), T243) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117^1(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> F655_IN(s(s(s(s(s(0))))), T1851) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118^1(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) F487_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> F655_IN(s(s(s(s(s(0))))), T1851) F487_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119^1(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) F487_IN(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> F655_IN(s(s(s(s(0)))), T1869) F487_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120^1(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) F487_IN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> F655_IN(s(s(s(s(0)))), T1869) F487_IN(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121^1(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) F487_IN(s(s(s(s(s(s(s(s(0)))))))), T1887) -> F655_IN(s(s(s(0))), T1887) F487_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122^1(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) F487_IN(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> F655_IN(s(s(s(0))), T1887) F487_IN(s(s(s(s(s(s(0)))))), T1905) -> U123^1(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) F487_IN(s(s(s(s(s(s(0)))))), T1905) -> F655_IN(s(s(0)), T1905) F487_IN(s(s(s(s(s(s(s(0))))))), T1905) -> U124^1(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) F487_IN(s(s(s(s(s(s(s(0))))))), T1905) -> F655_IN(s(s(0)), T1905) F487_IN(s(s(s(s(0)))), T1921) -> U125^1(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) F487_IN(s(s(s(s(0)))), T1921) -> F655_IN(s(0), T1921) F487_IN(s(s(s(s(s(0))))), T1921) -> U126^1(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) F487_IN(s(s(s(s(s(0))))), T1921) -> F655_IN(s(0), T1921) F487_IN(s(s(0)), T1934) -> U127^1(f655_in(0, T1934), s(s(0)), T1934) F487_IN(s(s(0)), T1934) -> F655_IN(0, T1934) F487_IN(s(s(s(0))), T1934) -> U128^1(f655_in(0, T1934), s(s(s(0))), T1934) F487_IN(s(s(s(0))), T1934) -> F655_IN(0, T1934) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (57) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 8 SCCs with 238 less nodes. ---------------------------------------- (58) Complex Obligation (AND) ---------------------------------------- (59) Obligation: Q DP problem: The TRS P consists of the following rules: F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> F1608_IN(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038) F1608_IN(s(s(T1063)), T1064, T1065, T1066) -> F1608_IN(T1063, s(T1064), T1065, T1066) F1608_IN(0, s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) F1608_IN(s(0), s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (60) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> F1608_IN(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038) F1608_IN(s(s(T1063)), T1064, T1065, T1066) -> F1608_IN(T1063, s(T1064), T1065, T1066) F1608_IN(0, s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) F1608_IN(s(0), s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: F1442_IN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> F1608_IN(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038) F1608_IN(s(s(T1063)), T1064, T1065, T1066) -> F1608_IN(T1063, s(T1064), T1065, T1066) F1608_IN(0, s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) F1608_IN(s(0), s(T1088), T1089, T1090) -> F1442_IN(T1088, s(T1089), T1090) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(F1442_IN(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(F1608_IN(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(s(x_1)) = 1 + x_1 ---------------------------------------- (63) Obligation: Q DP problem: P is empty. R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (65) YES ---------------------------------------- (66) Obligation: Q DP problem: The TRS P consists of the following rules: F1416_IN(s(s(T887)), T888, T889) -> F1416_IN(T887, s(T888), T889) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (67) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (68) Obligation: Q DP problem: The TRS P consists of the following rules: F1416_IN(s(s(T887)), T888, T889) -> F1416_IN(T887, s(T888), T889) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (69) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F1416_IN(s(s(T887)), T888, T889) -> F1416_IN(T887, s(T888), T889) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (70) YES ---------------------------------------- (71) Obligation: Q DP problem: The TRS P consists of the following rules: F1241_IN(s(s(T762)), T763, T764) -> F1241_IN(T762, s(T763), T764) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (72) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (73) Obligation: Q DP problem: The TRS P consists of the following rules: F1241_IN(s(s(T762)), T763, T764) -> F1241_IN(T762, s(T763), T764) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (74) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F1241_IN(s(s(T762)), T763, T764) -> F1241_IN(T762, s(T763), T764) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (75) YES ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: F1045_IN(s(s(T637)), T638, T639) -> F1045_IN(T637, s(T638), T639) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (78) Obligation: Q DP problem: The TRS P consists of the following rules: F1045_IN(s(s(T637)), T638, T639) -> F1045_IN(T637, s(T638), T639) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (79) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F1045_IN(s(s(T637)), T638, T639) -> F1045_IN(T637, s(T638), T639) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (80) YES ---------------------------------------- (81) Obligation: Q DP problem: The TRS P consists of the following rules: F902_IN(s(s(T512)), T513, T514) -> F902_IN(T512, s(T513), T514) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (82) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (83) Obligation: Q DP problem: The TRS P consists of the following rules: F902_IN(s(s(T512)), T513, T514) -> F902_IN(T512, s(T513), T514) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (84) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F902_IN(s(s(T512)), T513, T514) -> F902_IN(T512, s(T513), T514) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (85) YES ---------------------------------------- (86) Obligation: Q DP problem: The TRS P consists of the following rules: F752_IN(s(s(T387)), T388, T389) -> F752_IN(T387, s(T388), T389) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (87) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: F752_IN(s(s(T387)), T388, T389) -> F752_IN(T387, s(T388), T389) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (89) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F752_IN(s(s(T387)), T388, T389) -> F752_IN(T387, s(T388), T389) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (90) YES ---------------------------------------- (91) Obligation: Q DP problem: The TRS P consists of the following rules: F589_IN(s(s(T262)), T263, T264) -> F589_IN(T262, s(T263), T264) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: F589_IN(s(s(T262)), T263, T264) -> F589_IN(T262, s(T263), T264) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F589_IN(s(s(T262)), T263, T264) -> F589_IN(T262, s(T263), T264) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (95) YES ---------------------------------------- (96) Obligation: Q DP problem: The TRS P consists of the following rules: F430_IN(T136, T137) -> F430_IN(s(T136), T137) The TRS R consists of the following rules: f3_in(T115) -> U1(f430_in(s(s(s(s(s(s(s(0))))))), T115), T115) U1(f430_out1(T116), T115) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T116))))))))))))))))) f3_in(T1964) -> U2(f487_in(s(s(s(s(s(0))))), T1964), T1964) U2(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))) f3_in(T1964) -> U3(f487_in(s(s(s(s(s(0))))), T1964), T1964) U3(f487_out1, T1964) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))))) f3_in(T1986) -> U4(f487_in(s(s(s(s(0)))), T1986), T1986) U4(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))) f3_in(T1986) -> U5(f487_in(s(s(s(s(0)))), T1986), T1986) U5(f487_out1, T1986) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))) f3_in(T2008) -> U6(f487_in(s(s(s(0))), T2008), T2008) U6(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(0))))))))))) f3_in(T2008) -> U7(f487_in(s(s(s(0))), T2008), T2008) U7(f487_out1, T2008) -> f3_out1(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))) f3_in(T2030) -> U8(f487_in(s(s(0)), T2030), T2030) U8(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(0))))))))) f3_in(T2030) -> U9(f487_in(s(s(0)), T2030), T2030) U9(f487_out1, T2030) -> f3_out1(s(s(s(s(s(s(s(s(s(0)))))))))) f3_in(T2050) -> U10(f487_in(s(0), T2050), T2050) U10(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(0))))))) f3_in(T2050) -> U11(f487_in(s(0), T2050), T2050) U11(f487_out1, T2050) -> f3_out1(s(s(s(s(s(s(s(0)))))))) f3_in(T2067) -> U12(f487_in(0, T2067), T2067) U12(f487_out1, T2067) -> f3_out1(s(s(s(s(0))))) f3_in(T2067) -> U13(f487_in(0, T2067), T2067) U13(f487_out1, T2067) -> f3_out1(s(s(s(s(s(0)))))) f3_in(s(0)) -> f3_out1(s(s(0))) f3_in(s(0)) -> f3_out1(s(s(s(0)))) f3_in(s(0)) -> f3_out1(0) f3_in(s(0)) -> f3_out1(s(0)) f430_in(T136, T137) -> U14(f430_in(s(T136), T137), T136, T137) U14(f430_out1(T138), T136, T137) -> f430_out1(s(s(T138))) f430_in(s(T155), T156) -> U15(f487_in(T155, T156), s(T155), T156) U15(f487_out1, s(T155), T156) -> f430_out1(0) f430_in(s(T155), T156) -> U16(f487_in(T155, T156), s(T155), T156) U16(f487_out1, s(T155), T156) -> f430_out1(s(0)) f430_in(0, s(0)) -> f430_out1(0) f430_in(0, s(0)) -> f430_out1(s(0)) f589_in(s(s(T262)), T263, T264) -> U17(f589_in(T262, s(T263), T264), s(s(T262)), T263, T264) U17(f589_out1, s(s(T262)), T263, T264) -> f589_out1 f589_in(0, s(T281), T282) -> U18(f655_in(T281, T282), 0, s(T281), T282) U18(f655_out1, 0, s(T281), T282) -> f589_out1 f589_in(s(0), s(T281), T282) -> U19(f655_in(T281, T282), s(0), s(T281), T282) U19(f655_out1, s(0), s(T281), T282) -> f589_out1 f589_in(0, 0, s(s(0))) -> f589_out1 f589_in(s(0), 0, s(s(0))) -> f589_out1 f752_in(s(s(T387)), T388, T389) -> U20(f752_in(T387, s(T388), T389), s(s(T387)), T388, T389) U20(f752_out1, s(s(T387)), T388, T389) -> f752_out1 f752_in(0, s(T406), T407) -> U21(f786_in(T406, T407), 0, s(T406), T407) U21(f786_out1, 0, s(T406), T407) -> f752_out1 f752_in(s(0), s(T406), T407) -> U22(f786_in(T406, T407), s(0), s(T406), T407) U22(f786_out1, s(0), s(T406), T407) -> f752_out1 f752_in(0, 0, s(s(s(0)))) -> f752_out1 f752_in(s(0), 0, s(s(s(0)))) -> f752_out1 f902_in(s(s(T512)), T513, T514) -> U23(f902_in(T512, s(T513), T514), s(s(T512)), T513, T514) U23(f902_out1, s(s(T512)), T513, T514) -> f902_out1 f902_in(0, s(T531), T532) -> U24(f931_in(T531, T532), 0, s(T531), T532) U24(f931_out1, 0, s(T531), T532) -> f902_out1 f902_in(s(0), s(T531), T532) -> U25(f931_in(T531, T532), s(0), s(T531), T532) U25(f931_out1, s(0), s(T531), T532) -> f902_out1 f902_in(0, 0, s(s(s(s(0))))) -> f902_out1 f902_in(s(0), 0, s(s(s(s(0))))) -> f902_out1 f1045_in(s(s(T637)), T638, T639) -> U26(f1045_in(T637, s(T638), T639), s(s(T637)), T638, T639) U26(f1045_out1, s(s(T637)), T638, T639) -> f1045_out1 f1045_in(0, s(T656), T657) -> U27(f1094_in(T656, T657), 0, s(T656), T657) U27(f1094_out1, 0, s(T656), T657) -> f1045_out1 f1045_in(s(0), s(T656), T657) -> U28(f1094_in(T656, T657), s(0), s(T656), T657) U28(f1094_out1, s(0), s(T656), T657) -> f1045_out1 f1045_in(0, 0, s(s(s(s(s(0)))))) -> f1045_out1 f1045_in(s(0), 0, s(s(s(s(s(0)))))) -> f1045_out1 f1241_in(s(s(T762)), T763, T764) -> U29(f1241_in(T762, s(T763), T764), s(s(T762)), T763, T764) U29(f1241_out1, s(s(T762)), T763, T764) -> f1241_out1 f1241_in(0, s(T781), T782) -> U30(f1286_in(T781, T782), 0, s(T781), T782) U30(f1286_out1, 0, s(T781), T782) -> f1241_out1 f1241_in(s(0), s(T781), T782) -> U31(f1286_in(T781, T782), s(0), s(T781), T782) U31(f1286_out1, s(0), s(T781), T782) -> f1241_out1 f1241_in(0, 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1241_in(s(0), 0, s(s(s(s(s(s(0))))))) -> f1241_out1 f1416_in(s(s(T887)), T888, T889) -> U32(f1416_in(T887, s(T888), T889), s(s(T887)), T888, T889) U32(f1416_out1, s(s(T887)), T888, T889) -> f1416_out1 f1416_in(0, s(T906), T907) -> U33(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), 0, s(T906), T907) U33(f1442_out1, 0, s(T906), T907) -> f1416_out1 f1416_in(s(0), s(T906), T907) -> U34(f1442_in(T906, s(s(s(s(s(s(s(0))))))), T907), s(0), s(T906), T907) U34(f1442_out1, s(0), s(T906), T907) -> f1416_out1 f1416_in(0, 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1416_in(s(0), 0, s(s(s(s(s(s(s(0)))))))) -> f1416_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> U35(f1608_in(T1036, s(s(s(s(s(s(s(0))))))), T1037, T1038), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) U35(f1608_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T1036)))))))))))))), T1037, T1038) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> U36(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) U36(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> U37(f1442_in(s(s(s(s(s(0))))), s(T1126), T1127), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) U37(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1126, T1127) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> U38(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) U38(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> U39(f1442_in(s(s(s(s(0)))), s(T1157), T1158), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) U39(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1157, T1158) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> U40(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) U40(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> U41(f1442_in(s(s(s(0))), s(T1188), T1189), s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) U41(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1188, T1189) -> f1442_out1 f1442_in(s(s(s(s(s(s(0)))))), T1219, T1220) -> U42(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(0)))))), T1219, T1220) U42(f1442_out1, s(s(s(s(s(s(0)))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(s(s(s(0))))))), T1219, T1220) -> U43(f1442_in(s(s(0)), s(T1219), T1220), s(s(s(s(s(s(s(0))))))), T1219, T1220) U43(f1442_out1, s(s(s(s(s(s(s(0))))))), T1219, T1220) -> f1442_out1 f1442_in(s(s(s(s(0)))), T1246, T1247) -> U44(f1442_in(s(0), s(T1246), T1247), s(s(s(s(0)))), T1246, T1247) U44(f1442_out1, s(s(s(s(0)))), T1246, T1247) -> f1442_out1 f1442_in(s(s(s(s(s(0))))), T1246, T1247) -> U45(f1442_in(s(0), s(T1246), T1247), s(s(s(s(s(0))))), T1246, T1247) U45(f1442_out1, s(s(s(s(s(0))))), T1246, T1247) -> f1442_out1 f1442_in(s(s(0)), T1267, T1268) -> U46(f1442_in(0, s(T1267), T1268), s(s(0)), T1267, T1268) U46(f1442_out1, s(s(0)), T1267, T1268) -> f1442_out1 f1442_in(s(s(s(0))), T1267, T1268) -> U47(f1442_in(0, s(T1267), T1268), s(s(s(0))), T1267, T1268) U47(f1442_out1, s(s(s(0))), T1267, T1268) -> f1442_out1 f1442_in(0, T1281, s(T1281)) -> f1442_out1 f1442_in(s(0), T1281, s(T1281)) -> f1442_out1 f1608_in(s(s(T1063)), T1064, T1065, T1066) -> U48(f1608_in(T1063, s(T1064), T1065, T1066), s(s(T1063)), T1064, T1065, T1066) U48(f1608_out1, s(s(T1063)), T1064, T1065, T1066) -> f1608_out1 f1608_in(0, s(T1088), T1089, T1090) -> U49(f1442_in(T1088, s(T1089), T1090), 0, s(T1088), T1089, T1090) U49(f1442_out1, 0, s(T1088), T1089, T1090) -> f1608_out1 f1608_in(s(0), s(T1088), T1089, T1090) -> U50(f1442_in(T1088, s(T1089), T1090), s(0), s(T1088), T1089, T1090) U50(f1442_out1, s(0), s(T1088), T1089, T1090) -> f1608_out1 f1608_in(0, 0, T1108, s(T1108)) -> f1608_out1 f1608_in(s(0), 0, T1108, s(T1108)) -> f1608_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> U51(f1416_in(T867, s(s(s(s(s(s(s(0))))))), T868), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) U51(f1416_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T867)))))))))))))), T868) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> U52(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) U52(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> U53(f1442_in(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T1301), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) U53(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1301) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> U54(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) U54(f1442_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> U55(f1442_in(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T1319), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) U55(f1442_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1319) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(0)))))))), T1337) -> U56(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(0)))))))), T1337) U56(f1442_out1, s(s(s(s(s(s(s(s(0)))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> U57(f1442_in(s(s(s(0))), s(s(s(s(s(s(s(0))))))), T1337), s(s(s(s(s(s(s(s(s(0))))))))), T1337) U57(f1442_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1337) -> f1286_out1 f1286_in(s(s(s(s(s(s(0)))))), T1355) -> U58(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(0)))))), T1355) U58(f1442_out1, s(s(s(s(s(s(0)))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(s(s(s(0))))))), T1355) -> U59(f1442_in(s(s(0)), s(s(s(s(s(s(s(0))))))), T1355), s(s(s(s(s(s(s(0))))))), T1355) U59(f1442_out1, s(s(s(s(s(s(s(0))))))), T1355) -> f1286_out1 f1286_in(s(s(s(s(0)))), T1371) -> U60(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(0)))), T1371) U60(f1442_out1, s(s(s(s(0)))), T1371) -> f1286_out1 f1286_in(s(s(s(s(s(0))))), T1371) -> U61(f1442_in(s(0), s(s(s(s(s(s(s(0))))))), T1371), s(s(s(s(s(0))))), T1371) U61(f1442_out1, s(s(s(s(s(0))))), T1371) -> f1286_out1 f1286_in(s(s(0)), T1384) -> U62(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(0)), T1384) U62(f1442_out1, s(s(0)), T1384) -> f1286_out1 f1286_in(s(s(s(0))), T1384) -> U63(f1442_in(0, s(s(s(s(s(s(s(0))))))), T1384), s(s(s(0))), T1384) U63(f1442_out1, s(s(s(0))), T1384) -> f1286_out1 f1286_in(0, s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1286_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f1286_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> U64(f1241_in(T742, s(s(s(s(s(s(s(0))))))), T743), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) U64(f1241_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T742)))))))))))))), T743) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> U65(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) U65(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> U66(f1286_in(s(s(s(s(s(0))))), T1411), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) U66(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1411) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> U67(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) U67(f1286_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> U68(f1286_in(s(s(s(s(0)))), T1429), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) U68(f1286_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1429) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(0)))))))), T1447) -> U69(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(0)))))))), T1447) U69(f1286_out1, s(s(s(s(s(s(s(s(0)))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> U70(f1286_in(s(s(s(0))), T1447), s(s(s(s(s(s(s(s(s(0))))))))), T1447) U70(f1286_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1447) -> f1094_out1 f1094_in(s(s(s(s(s(s(0)))))), T1465) -> U71(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(0)))))), T1465) U71(f1286_out1, s(s(s(s(s(s(0)))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(s(s(s(0))))))), T1465) -> U72(f1286_in(s(s(0)), T1465), s(s(s(s(s(s(s(0))))))), T1465) U72(f1286_out1, s(s(s(s(s(s(s(0))))))), T1465) -> f1094_out1 f1094_in(s(s(s(s(0)))), T1481) -> U73(f1286_in(s(0), T1481), s(s(s(s(0)))), T1481) U73(f1286_out1, s(s(s(s(0)))), T1481) -> f1094_out1 f1094_in(s(s(s(s(s(0))))), T1481) -> U74(f1286_in(s(0), T1481), s(s(s(s(s(0))))), T1481) U74(f1286_out1, s(s(s(s(s(0))))), T1481) -> f1094_out1 f1094_in(s(s(0)), T1494) -> U75(f1286_in(0, T1494), s(s(0)), T1494) U75(f1286_out1, s(s(0)), T1494) -> f1094_out1 f1094_in(s(s(s(0))), T1494) -> U76(f1286_in(0, T1494), s(s(s(0))), T1494) U76(f1286_out1, s(s(s(0))), T1494) -> f1094_out1 f1094_in(0, s(s(s(s(s(s(0))))))) -> f1094_out1 f1094_in(s(0), s(s(s(s(s(s(0))))))) -> f1094_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> U77(f1045_in(T617, s(s(s(s(s(s(s(0))))))), T618), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) U77(f1045_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T617)))))))))))))), T618) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> U78(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) U78(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> U79(f1094_in(s(s(s(s(s(0))))), T1521), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) U79(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1521) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> U80(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) U80(f1094_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> U81(f1094_in(s(s(s(s(0)))), T1539), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) U81(f1094_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1539) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(0)))))))), T1557) -> U82(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(0)))))))), T1557) U82(f1094_out1, s(s(s(s(s(s(s(s(0)))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> U83(f1094_in(s(s(s(0))), T1557), s(s(s(s(s(s(s(s(s(0))))))))), T1557) U83(f1094_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1557) -> f931_out1 f931_in(s(s(s(s(s(s(0)))))), T1575) -> U84(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(0)))))), T1575) U84(f1094_out1, s(s(s(s(s(s(0)))))), T1575) -> f931_out1 f931_in(s(s(s(s(s(s(s(0))))))), T1575) -> U85(f1094_in(s(s(0)), T1575), s(s(s(s(s(s(s(0))))))), T1575) U85(f1094_out1, s(s(s(s(s(s(s(0))))))), T1575) -> f931_out1 f931_in(s(s(s(s(0)))), T1591) -> U86(f1094_in(s(0), T1591), s(s(s(s(0)))), T1591) U86(f1094_out1, s(s(s(s(0)))), T1591) -> f931_out1 f931_in(s(s(s(s(s(0))))), T1591) -> U87(f1094_in(s(0), T1591), s(s(s(s(s(0))))), T1591) U87(f1094_out1, s(s(s(s(s(0))))), T1591) -> f931_out1 f931_in(s(s(0)), T1604) -> U88(f1094_in(0, T1604), s(s(0)), T1604) U88(f1094_out1, s(s(0)), T1604) -> f931_out1 f931_in(s(s(s(0))), T1604) -> U89(f1094_in(0, T1604), s(s(s(0))), T1604) U89(f1094_out1, s(s(s(0))), T1604) -> f931_out1 f931_in(0, s(s(s(s(s(0)))))) -> f931_out1 f931_in(s(0), s(s(s(s(s(0)))))) -> f931_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> U90(f902_in(T492, s(s(s(s(s(s(s(0))))))), T493), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) U90(f902_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T492)))))))))))))), T493) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> U91(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) U91(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> U92(f931_in(s(s(s(s(s(0))))), T1631), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) U92(f931_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1631) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> U93(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) U93(f931_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> U94(f931_in(s(s(s(s(0)))), T1649), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) U94(f931_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1649) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(0)))))))), T1667) -> U95(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(0)))))))), T1667) U95(f931_out1, s(s(s(s(s(s(s(s(0)))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> U96(f931_in(s(s(s(0))), T1667), s(s(s(s(s(s(s(s(s(0))))))))), T1667) U96(f931_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1667) -> f786_out1 f786_in(s(s(s(s(s(s(0)))))), T1685) -> U97(f931_in(s(s(0)), T1685), s(s(s(s(s(s(0)))))), T1685) U97(f931_out1, s(s(s(s(s(s(0)))))), T1685) -> f786_out1 f786_in(s(s(s(s(s(s(s(0))))))), T1685) -> U98(f931_in(s(s(0)), T1685), s(s(s(s(s(s(s(0))))))), T1685) U98(f931_out1, s(s(s(s(s(s(s(0))))))), T1685) -> f786_out1 f786_in(s(s(s(s(0)))), T1701) -> U99(f931_in(s(0), T1701), s(s(s(s(0)))), T1701) U99(f931_out1, s(s(s(s(0)))), T1701) -> f786_out1 f786_in(s(s(s(s(s(0))))), T1701) -> U100(f931_in(s(0), T1701), s(s(s(s(s(0))))), T1701) U100(f931_out1, s(s(s(s(s(0))))), T1701) -> f786_out1 f786_in(s(s(0)), T1714) -> U101(f931_in(0, T1714), s(s(0)), T1714) U101(f931_out1, s(s(0)), T1714) -> f786_out1 f786_in(s(s(s(0))), T1714) -> U102(f931_in(0, T1714), s(s(s(0))), T1714) U102(f931_out1, s(s(s(0))), T1714) -> f786_out1 f786_in(0, s(s(s(s(0))))) -> f786_out1 f786_in(s(0), s(s(s(s(0))))) -> f786_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> U103(f752_in(T367, s(s(s(s(s(s(s(0))))))), T368), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) U103(f752_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T367)))))))))))))), T368) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> U104(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) U104(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> U105(f786_in(s(s(s(s(s(0))))), T1741), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) U105(f786_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1741) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> U106(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) U106(f786_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> U107(f786_in(s(s(s(s(0)))), T1759), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) U107(f786_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1759) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(0)))))))), T1777) -> U108(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(0)))))))), T1777) U108(f786_out1, s(s(s(s(s(s(s(s(0)))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> U109(f786_in(s(s(s(0))), T1777), s(s(s(s(s(s(s(s(s(0))))))))), T1777) U109(f786_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1777) -> f655_out1 f655_in(s(s(s(s(s(s(0)))))), T1795) -> U110(f786_in(s(s(0)), T1795), s(s(s(s(s(s(0)))))), T1795) U110(f786_out1, s(s(s(s(s(s(0)))))), T1795) -> f655_out1 f655_in(s(s(s(s(s(s(s(0))))))), T1795) -> U111(f786_in(s(s(0)), T1795), s(s(s(s(s(s(s(0))))))), T1795) U111(f786_out1, s(s(s(s(s(s(s(0))))))), T1795) -> f655_out1 f655_in(s(s(s(s(0)))), T1811) -> U112(f786_in(s(0), T1811), s(s(s(s(0)))), T1811) U112(f786_out1, s(s(s(s(0)))), T1811) -> f655_out1 f655_in(s(s(s(s(s(0))))), T1811) -> U113(f786_in(s(0), T1811), s(s(s(s(s(0))))), T1811) U113(f786_out1, s(s(s(s(s(0))))), T1811) -> f655_out1 f655_in(s(s(0)), T1824) -> U114(f786_in(0, T1824), s(s(0)), T1824) U114(f786_out1, s(s(0)), T1824) -> f655_out1 f655_in(s(s(s(0))), T1824) -> U115(f786_in(0, T1824), s(s(s(0))), T1824) U115(f786_out1, s(s(s(0))), T1824) -> f655_out1 f655_in(0, s(s(s(0)))) -> f655_out1 f655_in(s(0), s(s(s(0)))) -> f655_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> U116(f589_in(T242, s(s(s(s(s(s(s(0))))))), T243), s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) U116(f589_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(s(T242)))))))))))))), T243) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> U117(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) U117(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> U118(f655_in(s(s(s(s(s(0))))), T1851), s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) U118(f655_out1, s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), T1851) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> U119(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) U119(f655_out1, s(s(s(s(s(s(s(s(s(s(0)))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> U120(f655_in(s(s(s(s(0)))), T1869), s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) U120(f655_out1, s(s(s(s(s(s(s(s(s(s(s(0))))))))))), T1869) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(0)))))))), T1887) -> U121(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(0)))))))), T1887) U121(f655_out1, s(s(s(s(s(s(s(s(0)))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> U122(f655_in(s(s(s(0))), T1887), s(s(s(s(s(s(s(s(s(0))))))))), T1887) U122(f655_out1, s(s(s(s(s(s(s(s(s(0))))))))), T1887) -> f487_out1 f487_in(s(s(s(s(s(s(0)))))), T1905) -> U123(f655_in(s(s(0)), T1905), s(s(s(s(s(s(0)))))), T1905) U123(f655_out1, s(s(s(s(s(s(0)))))), T1905) -> f487_out1 f487_in(s(s(s(s(s(s(s(0))))))), T1905) -> U124(f655_in(s(s(0)), T1905), s(s(s(s(s(s(s(0))))))), T1905) U124(f655_out1, s(s(s(s(s(s(s(0))))))), T1905) -> f487_out1 f487_in(s(s(s(s(0)))), T1921) -> U125(f655_in(s(0), T1921), s(s(s(s(0)))), T1921) U125(f655_out1, s(s(s(s(0)))), T1921) -> f487_out1 f487_in(s(s(s(s(s(0))))), T1921) -> U126(f655_in(s(0), T1921), s(s(s(s(s(0))))), T1921) U126(f655_out1, s(s(s(s(s(0))))), T1921) -> f487_out1 f487_in(s(s(0)), T1934) -> U127(f655_in(0, T1934), s(s(0)), T1934) U127(f655_out1, s(s(0)), T1934) -> f487_out1 f487_in(s(s(s(0))), T1934) -> U128(f655_in(0, T1934), s(s(s(0))), T1934) U128(f655_out1, s(s(s(0))), T1934) -> f487_out1 f487_in(0, s(s(0))) -> f487_out1 f487_in(s(0), s(s(0))) -> f487_out1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (97) UsableRulesProof (EQUIVALENT) We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (98) Obligation: Q DP problem: The TRS P consists of the following rules: F430_IN(T136, T137) -> F430_IN(s(T136), T137) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (99) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule F430_IN(T136, T137) -> F430_IN(s(T136), T137) we obtained the following new rules [LPAR04]: (F430_IN(s(z0), z1) -> F430_IN(s(s(z0)), z1),F430_IN(s(z0), z1) -> F430_IN(s(s(z0)), z1)) ---------------------------------------- (100) Obligation: Q DP problem: The TRS P consists of the following rules: F430_IN(s(z0), z1) -> F430_IN(s(s(z0)), z1) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (101) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule F430_IN(s(z0), z1) -> F430_IN(s(s(z0)), z1) we obtained the following new rules [LPAR04]: (F430_IN(s(s(z0)), z1) -> F430_IN(s(s(s(z0))), z1),F430_IN(s(s(z0)), z1) -> F430_IN(s(s(s(z0))), z1)) ---------------------------------------- (102) Obligation: Q DP problem: The TRS P consists of the following rules: F430_IN(s(s(z0)), z1) -> F430_IN(s(s(s(z0))), z1) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (103) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = F430_IN(s(s(z0)), z1) evaluates to t =F430_IN(s(s(s(z0))), z1) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [z0 / s(z0)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from F430_IN(s(s(z0)), z1) to F430_IN(s(s(s(z0))), z1). ---------------------------------------- (104) NO ---------------------------------------- (105) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(log2 X Y)", "(log2 X (0) (s (0)) Y)" ], [ "(log2 (s (s X)) Half Acc Y)", "(log2 X (s Half) Acc Y)" ], [ "(log2 X (s (s Half)) Acc Y)", "(',' (small X) (log2 Half (s (0)) (s Acc) Y))" ], [ "(log2 X Half Y Y)", "(',' (small X) (small Half))" ], [ "(small (0))", null ], [ "(small (s (0)))", null ] ] }, "graph": { "nodes": { "4971": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (small T1803) (log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1803", "T1804" ], "free": [], "exprvars": [] } }, "1462": { "goal": [ { "clause": 1, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" }, { "clause": 2, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" }, { "clause": 3, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T993", "T994", "T995" ], "free": [], "exprvars": [] } }, "1459": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1458": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T993", "T994", "T995" ], "free": [], "exprvars": [] } }, "5817": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (small T1965) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5818": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2787": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5819": { "goal": [ { "clause": 4, "scope": 289, "term": "(',' (small T1965) (small (s (s (s (s (s (s (s (0))))))))))" }, { "clause": 5, "scope": 289, "term": "(',' (small T1965) (small (s (s (s (s (s (s (s (0))))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2786": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1364"], "free": [], "exprvars": [] } }, "1454": { "goal": [ { "clause": 2, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" }, { "clause": 3, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T975", "T976", "T977" ], "free": [], "exprvars": [] } }, "2785": { "goal": [{ "clause": 5, "scope": 124, "term": "(',' (small T1363) (log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1363", "T1364" ], "free": [], "exprvars": [] } }, "1453": { "goal": [{ "clause": 1, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T975", "T976", "T977" ], "free": [], "exprvars": [] } }, "2784": { "goal": [{ "clause": 4, "scope": 124, "term": "(',' (small T1363) (log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1363", "T1364" ], "free": [], "exprvars": [] } }, "1452": { "goal": [ { "clause": 1, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" }, { "clause": 2, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" }, { "clause": 3, "scope": 70, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T975", "T976", "T977" ], "free": [], "exprvars": [] } }, "2783": { "goal": [ { "clause": 4, "scope": 124, "term": "(',' (small T1363) (log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364))" }, { "clause": 5, "scope": 124, "term": "(',' (small T1363) (log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1363", "T1364" ], "free": [], "exprvars": [] } }, "5810": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1957"], "free": [], "exprvars": [] } }, "5811": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5812": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1957"], "free": [], "exprvars": [] } }, "5813": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1472": { "goal": [ { "clause": 1, "scope": 72, "term": "(log2 T1011 (s (s (s (s (s (s (s (0)))))))) (s T1012) T1013)" }, { "clause": 2, "scope": 72, "term": "(log2 T1011 (s (s (s (s (s (s (s (0)))))))) (s T1012) T1013)" }, { "clause": 3, "scope": 72, "term": "(log2 T1011 (s (s (s (s (s (s (s (0)))))))) (s T1012) T1013)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1011", "T1012", "T1013" ], "free": [], "exprvars": [] } }, "2317": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (small T1266) (small (s (s (0)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1266"], "free": [], "exprvars": [] } }, "5827": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T2"], "free": [], "exprvars": [] } }, "1469": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5828": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1468": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 T1011 (s (s (s (s (s (s (s (0)))))))) (s T1012) T1013)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1011", "T1012", "T1013" ], "free": [], "exprvars": [] } }, "5829": { "goal": [ { "clause": 4, "scope": 291, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }, { "clause": 5, "scope": 291, "term": "(small (s (s (s (s (s (s (s (0)))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1466": { "goal": [ { "clause": 2, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" }, { "clause": 3, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T993", "T994", "T995" ], "free": [], "exprvars": [] } }, "1465": { "goal": [{ "clause": 1, "scope": 71, "term": "(log2 T993 (s (s (s (s (s (s (0))))))) (s T994) T995)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T993", "T994", "T995" ], "free": [], "exprvars": [] } }, "6": { "goal": [{ "clause": 0, "scope": 1, "term": "(log2 T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T2"], "free": [], "exprvars": [] } }, "4972": { "goal": [ { "clause": 4, "scope": 244, "term": "(',' (small T1803) (log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804))" }, { "clause": 5, "scope": 244, "term": "(',' (small T1803) (log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1803", "T1804" ], "free": [], "exprvars": [] } }, "4973": { "goal": [{ "clause": 4, "scope": 244, "term": "(',' (small T1803) (log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1803", "T1804" ], "free": [], "exprvars": [] } }, "5820": { "goal": [{ "clause": 4, "scope": 289, "term": "(',' (small T1965) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4974": { "goal": [{ "clause": 5, "scope": 244, "term": "(',' (small T1803) (log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1803", "T1804" ], "free": [], "exprvars": [] } }, "5821": { "goal": [{ "clause": 5, "scope": 289, "term": "(',' (small T1965) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4975": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 (s (0)) (s (0)) (s (s (s (s (0))))) T1804)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1804"], "free": [], "exprvars": [] } }, "5822": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4976": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5823": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5824": { "goal": [ { "clause": 4, "scope": 290, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }, { "clause": 5, "scope": 290, "term": "(small (s (s (s (s (s (s (s (0)))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2319": { "goal": [ { "clause": 4, 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"kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1420": { "goal": [ { "clause": 1, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" }, { "clause": 2, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" }, { "clause": 3, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T957", "T958", "T959" ], "free": [], "exprvars": [] } }, "2751": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2750": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (0))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1440": { "goal": [{ "clause": -1, "scope": -1, "term": "(log2 T975 (s (s (s (s (s (0)))))) (s T976) T977)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T975", "T976", "T977" ], "free": [], "exprvars": [] } }, "3615": { "goal": [{ "clause": 4, "scope": 169, "term": "(',' (small T1520) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1520"], "free": [], "exprvars": [] } }, "3614": { "goal": [ { "clause": 4, "scope": 169, "term": "(',' (small T1520) (small (s (s (s (s (s (s (s (0))))))))))" }, { "clause": 5, "scope": 169, "term": "(',' (small T1520) (small (s (s (s (s (s (s (s (0))))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1520"], "free": [], "exprvars": [] } }, "3613": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3612": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (small T1520) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1520"], "free": [], "exprvars": [] } }, "1432": { "goal": [ { "clause": 2, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" }, { "clause": 3, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T957", "T958", "T959" ], "free": [], "exprvars": [] } }, "1431": { "goal": [{ "clause": 1, "scope": 69, "term": "(log2 T957 (s (s (s (s (0))))) (s T958) T959)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T957", "T958", "T959" ], "free": [], "exprvars": [] } }, "3619": { "goal": [ { "clause": 4, "scope": 170, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }, { "clause": 5, "scope": 170, "term": "(small (s (s (s (s (s (s (s (0)))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3618": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3617": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3616": { "goal": [{ "clause": 5, "scope": 169, "term": "(',' (small T1520) (small (s (s (s (s (s (s (s (0))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1520"], "free": [], "exprvars": [] } }, "2782": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (small T1363) (log2 (s (0)) (s (0)) (s (s (s (s (s (s (s (s (0))))))))) T1364))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1363", "T1364" ], "free": [], "exprvars": [] } }, "3626": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3625": { "goal": [{ "clause": 5, "scope": 171, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3624": { "goal": [ { "clause": 4, "scope": 171, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }, { "clause": 5, "scope": 171, "term": "(small (s (s (s (s (s (s (s (0)))))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5807": { "goal": [ { "clause": 4, "scope": 288, "term": "(',' (small T1958) (log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957))" }, { "clause": 5, "scope": 288, "term": "(',' (small T1958) (log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1957"], "free": [], "exprvars": [] } }, "3623": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5808": { "goal": [{ "clause": 4, "scope": 288, "term": "(',' (small T1958) (log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1957"], "free": [], "exprvars": [] } }, "3622": { "goal": [{ "clause": -1, "scope": -1, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5809": { "goal": [{ "clause": 5, "scope": 288, "term": "(',' (small T1958) (log2 (s (s (s (s (s (0)))))) (s (0)) (s (s (0))) T1957))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1957"], "free": [], "exprvars": [] } }, "3621": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3620": { "goal": [{ "clause": 5, "scope": 170, "term": "(small (s (s (s (s (s (s (s (0)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1441": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 6, "label": "CASE" }, { "from": 6, "to": 21, "label": "ONLY EVAL with clause\nlog2(X3, X4) :- log2(X3, 0, s(0), X4).\nand substitutionT1 -> T7,\nX3 -> T7,\nT2 -> T6,\nX4 -> T6,\nT5 -> T7" }, { "from": 21, "to": 22, "label": "CASE" }, { "from": 22, "to": 23, "label": "PARALLEL" }, { "from": 22, "to": 24, "label": "PARALLEL" }, { "from": 23, "to": 39, "label": "EVAL with clause\nlog2(s(s(X21)), X22, X23, X24) :- log2(X21, s(X22), X23, X24).\nand substitutionX21 -> T18,\nT7 -> s(s(T18)),\nX22 -> 0,\nX23 -> s(0),\nT6 -> T17,\nX24 -> T17,\nT16 -> T18" }, { "from": 23, "to": 55, "label": "EVAL-BACKTRACK" }, { "from": 24, "to": 6275, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 39, "to": 201, "label": "CASE" }, { "from": 201, "to": 205, "label": "PARALLEL" }, { "from": 201, "to": 207, "label": "PARALLEL" }, { "from": 205, "to": 225, "label": "EVAL with clause\nlog2(s(s(X45)), X46, X47, X48) :- log2(X45, s(X46), X47, X48).\nand substitutionX45 -> T31,\nT18 -> s(s(T31)),\nX46 -> s(0),\nX47 -> s(0),\nT17 -> T30,\nX48 -> T30,\nT29 -> T31" }, { "from": 205, "to": 227, "label": "EVAL-BACKTRACK" }, { "from": 207, "to": 6257, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 225, "to": 239, "label": "CASE" }, { "from": 239, "to": 250, "label": "PARALLEL" }, { "from": 239, "to": 251, "label": "PARALLEL" }, { "from": 250, "to": 253, "label": "EVAL with clause\nlog2(s(s(X69)), X70, X71, X72) :- log2(X69, s(X70), X71, X72).\nand substitutionX69 -> T44,\nT31 -> s(s(T44)),\nX70 -> s(s(0)),\nX71 -> s(0),\nT30 -> T43,\nX72 -> T43,\nT42 -> T44" }, { "from": 250, "to": 254, "label": "EVAL-BACKTRACK" }, { "from": 251, "to": 6177, "label": "PARALLEL" }, { "from": 251, "to": 6178, "label": "PARALLEL" }, { "from": 253, "to": 283, "label": "CASE" }, { "from": 283, "to": 286, "label": "PARALLEL" }, { "from": 283, "to": 287, "label": "PARALLEL" }, { "from": 286, "to": 298, "label": "EVAL with clause\nlog2(s(s(X93)), X94, X95, X96) :- log2(X93, s(X94), X95, X96).\nand substitutionX93 -> T57,\nT44 -> s(s(T57)),\nX94 -> s(s(s(0))),\nX95 -> s(0),\nT43 -> T56,\nX96 -> T56,\nT55 -> T57" }, { "from": 286, "to": 299, "label": "EVAL-BACKTRACK" }, { "from": 287, "to": 6072, "label": "PARALLEL" }, { "from": 287, "to": 6073, "label": "PARALLEL" }, { "from": 298, "to": 300, "label": "CASE" }, { "from": 300, "to": 301, "label": "PARALLEL" }, { "from": 300, "to": 302, "label": "PARALLEL" }, { "from": 301, "to": 306, "label": "EVAL with clause\nlog2(s(s(X117)), X118, X119, X120) :- log2(X117, s(X118), X119, X120).\nand substitutionX117 -> T70,\nT57 -> s(s(T70)),\nX118 -> s(s(s(s(0)))),\nX119 -> s(0),\nT56 -> T69,\nX120 -> T69,\nT68 -> T70" }, { "from": 301, "to": 307, "label": "EVAL-BACKTRACK" }, { "from": 302, "to": 5997, "label": "PARALLEL" }, { "from": 302, "to": 5998, "label": "PARALLEL" }, { "from": 306, "to": 311, "label": "CASE" }, { "from": 311, "to": 314, "label": "PARALLEL" }, { "from": 311, "to": 315, "label": "PARALLEL" }, { "from": 314, "to": 321, "label": "EVAL with clause\nlog2(s(s(X141)), X142, X143, X144) :- log2(X141, s(X142), X143, X144).\nand substitutionX141 -> T83,\nT70 -> s(s(T83)),\nX142 -> s(s(s(s(s(0))))),\nX143 -> s(0),\nT69 -> T82,\nX144 -> T82,\nT81 -> T83" }, { "from": 314, "to": 322, "label": "EVAL-BACKTRACK" }, { "from": 315, "to": 5922, "label": "PARALLEL" }, { "from": 315, "to": 5923, "label": "PARALLEL" }, { "from": 321, "to": 328, "label": "CASE" }, { "from": 328, "to": 331, "label": "PARALLEL" }, { "from": 328, "to": 332, "label": "PARALLEL" }, { "from": 331, "to": 336, "label": "EVAL with clause\nlog2(s(s(X165)), X166, X167, X168) :- log2(X165, s(X166), X167, X168).\nand substitutionX165 -> T96,\nT83 -> s(s(T96)),\nX166 -> s(s(s(s(s(s(0)))))),\nX167 -> s(0),\nT82 -> T95,\nX168 -> T95,\nT94 -> T96" }, { "from": 331, "to": 337, "label": "EVAL-BACKTRACK" }, { "from": 332, "to": 5839, "label": "PARALLEL" }, { "from": 332, "to": 5840, "label": "PARALLEL" }, { "from": 336, "to": 343, "label": "CASE" }, { "from": 343, "to": 344, "label": "PARALLEL" }, { "from": 343, "to": 345, "label": "PARALLEL" }, { "from": 344, "to": 346, "label": "EVAL with clause\nlog2(s(s(X189)), X190, X191, X192) :- log2(X189, s(X190), X191, X192).\nand substitutionX189 -> T109,\nT96 -> s(s(T109)),\nX190 -> s(s(s(s(s(s(s(0))))))),\nX191 -> s(0),\nT95 -> T108,\nX192 -> T108,\nT107 -> T109" }, { "from": 344, "to": 347, "label": "EVAL-BACKTRACK" }, { "from": 345, "to": 5765, "label": "PARALLEL" }, { "from": 345, "to": 5766, "label": "PARALLEL" }, { "from": 346, "to": 349, "label": "GENERALIZATION\nT112 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT112 is ground" }, { "from": 349, "to": 352, "label": "CASE" }, { "from": 352, "to": 355, "label": "PARALLEL" }, { "from": 352, "to": 356, "label": "PARALLEL" }, { "from": 355, "to": 373, "label": "EVAL with clause\nlog2(s(s(X217)), X218, X219, X220) :- log2(X217, s(X218), X219, X220).\nand substitutionX217 -> T131,\nT109 -> s(s(T131)),\nT112 -> T129,\nX218 -> s(T129),\nX219 -> s(0),\nT108 -> T130,\nX220 -> T130,\nT128 -> T131" }, { "from": 355, "to": 383, "label": "EVAL-BACKTRACK" }, { "from": 356, "to": 386, "label": "PARALLEL" }, { "from": 356, "to": 387, "label": "PARALLEL" }, { "from": 373, "to": 349, "label": "INSTANCE with matching:\nT109 -> T131\nT112 -> s(T129)\nT108 -> T130" }, { "from": 386, "to": 388, "label": "EVAL with clause\nlog2(X241, s(s(X242)), X243, X244) :- ','(small(X241), log2(X242, s(0), s(X243), X244)).\nand substitutionT109 -> T150,\nX241 -> T150,\nX242 -> T148,\nT112 -> s(T148),\nX243 -> s(0),\nT108 -> T149,\nX244 -> T149,\nT147 -> T150" }, { "from": 386, "to": 389, "label": "EVAL-BACKTRACK" }, { "from": 387, "to": 5738, "label": "EVAL with clause\nlog2(X4075, X4076, X4077, X4077) :- ','(small(X4075), small(X4076)).\nand substitutionT109 -> T1943,\nX4075 -> T1943,\nT112 -> T1942,\nX4076 -> s(T1942),\nX4077 -> s(0),\nT108 -> s(0),\nT1941 -> T1943" }, { "from": 387, "to": 5739, "label": "EVAL-BACKTRACK" }, { "from": 388, "to": 390, "label": "CASE" }, { "from": 390, "to": 391, "label": "PARALLEL" }, { "from": 390, "to": 392, "label": "PARALLEL" }, { "from": 391, "to": 393, "label": "EVAL with clause\nsmall(0).\nand substitutionT150 -> 0" }, { "from": 391, "to": 394, "label": "EVAL-BACKTRACK" }, { "from": 392, "to": 5733, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT150 -> s(0)" }, { "from": 392, "to": 5734, "label": "EVAL-BACKTRACK" }, { "from": 393, "to": 395, "label": "CASE" }, { "from": 395, "to": 396, "label": "PARALLEL" }, { "from": 395, "to": 397, "label": "PARALLEL" }, { "from": 396, "to": 398, "label": "EVAL with clause\nlog2(s(s(X269)), X270, X271, X272) :- log2(X269, s(X270), X271, X272).\nand substitutionX269 -> T163,\nT148 -> s(s(T163)),\nX270 -> s(0),\nX271 -> s(s(0)),\nT149 -> T164,\nX272 -> T164" }, { "from": 396, "to": 399, "label": "EVAL-BACKTRACK" }, { "from": 397, "to": 5694, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 398, "to": 400, "label": "CASE" }, { "from": 400, "to": 401, "label": "PARALLEL" }, { "from": 400, "to": 402, "label": "PARALLEL" }, { "from": 401, "to": 445, "label": "EVAL with clause\nlog2(s(s(X293)), X294, X295, X296) :- log2(X293, s(X294), X295, X296).\nand substitutionX293 -> T175,\nT163 -> s(s(T175)),\nX294 -> s(s(0)),\nX295 -> s(s(0)),\nT164 -> T176,\nX296 -> T176" }, { "from": 401, "to": 446, "label": "EVAL-BACKTRACK" }, { "from": 402, "to": 5607, "label": "PARALLEL" }, { "from": 402, "to": 5608, "label": "PARALLEL" }, { "from": 445, "to": 449, "label": "CASE" }, { "from": 449, "to": 452, "label": "PARALLEL" }, { "from": 449, "to": 453, "label": "PARALLEL" }, { "from": 452, "to": 457, "label": "EVAL with clause\nlog2(s(s(X317)), X318, X319, X320) :- log2(X317, s(X318), X319, X320).\nand substitutionX317 -> T187,\nT175 -> s(s(T187)),\nX318 -> s(s(s(0))),\nX319 -> s(s(0)),\nT176 -> T188,\nX320 -> T188" }, { "from": 452, "to": 458, "label": "EVAL-BACKTRACK" }, { "from": 453, "to": 5489, "label": "PARALLEL" }, { "from": 453, "to": 5490, "label": "PARALLEL" }, { "from": 457, "to": 461, "label": "CASE" }, { "from": 461, "to": 462, "label": "PARALLEL" }, { "from": 461, "to": 463, "label": "PARALLEL" }, { "from": 462, "to": 467, "label": "EVAL with clause\nlog2(s(s(X341)), X342, X343, X344) :- log2(X341, s(X342), X343, X344).\nand substitutionX341 -> T199,\nT187 -> s(s(T199)),\nX342 -> s(s(s(s(0)))),\nX343 -> s(s(0)),\nT188 -> T200,\nX344 -> T200" }, { "from": 462, "to": 468, "label": "EVAL-BACKTRACK" }, { "from": 463, "to": 5414, "label": "PARALLEL" }, { "from": 463, "to": 5415, "label": "PARALLEL" }, { "from": 467, "to": 469, "label": "CASE" }, { "from": 469, "to": 470, "label": "PARALLEL" }, { "from": 469, "to": 471, "label": "PARALLEL" }, { "from": 470, "to": 472, "label": "EVAL with clause\nlog2(s(s(X365)), X366, X367, X368) :- log2(X365, s(X366), X367, X368).\nand substitutionX365 -> T211,\nT199 -> s(s(T211)),\nX366 -> s(s(s(s(s(0))))),\nX367 -> s(s(0)),\nT200 -> T212,\nX368 -> T212" }, { "from": 470, "to": 473, "label": "EVAL-BACKTRACK" }, { "from": 471, "to": 5341, "label": "PARALLEL" }, { "from": 471, "to": 5342, "label": "PARALLEL" }, { "from": 472, "to": 474, "label": "CASE" }, { "from": 474, "to": 475, "label": "PARALLEL" }, { "from": 474, "to": 476, "label": "PARALLEL" }, { "from": 475, "to": 477, "label": "EVAL with clause\nlog2(s(s(X389)), X390, X391, X392) :- log2(X389, s(X390), X391, X392).\nand substitutionX389 -> T223,\nT211 -> s(s(T223)),\nX390 -> s(s(s(s(s(s(0)))))),\nX391 -> s(s(0)),\nT212 -> T224,\nX392 -> T224" }, { "from": 475, "to": 480, "label": "EVAL-BACKTRACK" }, { "from": 476, "to": 5266, "label": "PARALLEL" }, { "from": 476, "to": 5267, "label": "PARALLEL" }, { "from": 477, "to": 482, "label": "CASE" }, { "from": 482, "to": 489, "label": "PARALLEL" }, { "from": 482, "to": 490, "label": "PARALLEL" }, { "from": 489, "to": 493, "label": "EVAL with clause\nlog2(s(s(X413)), X414, X415, X416) :- log2(X413, s(X414), X415, X416).\nand substitutionX413 -> T235,\nT223 -> s(s(T235)),\nX414 -> s(s(s(s(s(s(s(0))))))),\nX415 -> s(s(0)),\nT224 -> T236,\nX416 -> T236" }, { "from": 489, "to": 494, "label": "EVAL-BACKTRACK" }, { "from": 490, "to": 5196, "label": "PARALLEL" }, { "from": 490, "to": 5197, "label": "PARALLEL" }, { "from": 493, "to": 498, "label": "GENERALIZATION\nT239 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT239 is ground" }, { "from": 498, "to": 530, "label": "CASE" }, { "from": 530, "to": 539, "label": "PARALLEL" }, { "from": 530, "to": 540, "label": "PARALLEL" }, { "from": 539, "to": 541, "label": "EVAL with clause\nlog2(s(s(X441)), X442, X443, X444) :- log2(X441, s(X442), X443, X444).\nand substitutionX441 -> T255,\nT235 -> s(s(T255)),\nT239 -> T256,\nX442 -> s(T256),\nX443 -> s(s(0)),\nT236 -> T257,\nX444 -> T257" }, { "from": 539, "to": 542, "label": "EVAL-BACKTRACK" }, { "from": 540, "to": 546, "label": "PARALLEL" }, { "from": 540, "to": 547, "label": "PARALLEL" }, { "from": 541, "to": 498, "label": "INSTANCE with matching:\nT235 -> T255\nT239 -> s(T256)\nT236 -> T257" }, { "from": 546, "to": 552, "label": "EVAL with clause\nlog2(X465, s(s(X466)), X467, X468) :- ','(small(X465), log2(X466, s(0), s(X467), X468)).\nand substitutionT235 -> T273,\nX465 -> T273,\nX466 -> T274,\nT239 -> s(T274),\nX467 -> s(s(0)),\nT236 -> T275,\nX468 -> T275" }, { "from": 546, "to": 553, "label": "EVAL-BACKTRACK" }, { "from": 547, "to": 5170, "label": "EVAL with clause\nlog2(X3755, X3756, X3757, X3757) :- ','(small(X3755), small(X3756)).\nand substitutionT235 -> T1831,\nX3755 -> T1831,\nT239 -> T1832,\nX3756 -> s(T1832),\nX3757 -> s(s(0)),\nT236 -> s(s(0))" }, { "from": 547, "to": 5171, "label": "EVAL-BACKTRACK" }, { "from": 552, "to": 554, "label": "CASE" }, { "from": 554, "to": 558, "label": "PARALLEL" }, { "from": 554, "to": 559, "label": "PARALLEL" }, { "from": 558, "to": 560, "label": "EVAL with clause\nsmall(0).\nand substitutionT273 -> 0" }, { "from": 558, "to": 561, "label": "EVAL-BACKTRACK" }, { "from": 559, "to": 5164, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT273 -> s(0)" }, { "from": 559, "to": 5165, "label": "EVAL-BACKTRACK" }, { "from": 560, "to": 562, "label": "CASE" }, { "from": 562, "to": 563, "label": "PARALLEL" }, { "from": 562, "to": 564, "label": "PARALLEL" }, { "from": 563, "to": 569, "label": "EVAL with clause\nlog2(s(s(X493)), X494, X495, X496) :- log2(X493, s(X494), X495, X496).\nand substitutionX493 -> T288,\nT274 -> s(s(T288)),\nX494 -> s(0),\nX495 -> s(s(s(0))),\nT275 -> T289,\nX496 -> T289" }, { "from": 563, "to": 570, "label": "EVAL-BACKTRACK" }, { "from": 564, "to": 5112, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 569, "to": 574, "label": "CASE" }, { "from": 574, "to": 575, "label": "PARALLEL" }, { "from": 574, "to": 576, "label": "PARALLEL" }, { "from": 575, "to": 580, "label": "EVAL with clause\nlog2(s(s(X517)), X518, X519, X520) :- log2(X517, s(X518), X519, X520).\nand substitutionX517 -> T300,\nT288 -> s(s(T300)),\nX518 -> s(s(0)),\nX519 -> s(s(s(0))),\nT289 -> T301,\nX520 -> T301" }, { "from": 575, "to": 581, "label": "EVAL-BACKTRACK" }, { "from": 576, "to": 5042, "label": "PARALLEL" }, { "from": 576, "to": 5043, "label": "PARALLEL" }, { "from": 580, "to": 584, "label": "CASE" }, { "from": 584, "to": 587, "label": "PARALLEL" }, { "from": 584, "to": 588, "label": "PARALLEL" }, { "from": 587, "to": 590, "label": "EVAL with clause\nlog2(s(s(X541)), X542, X543, X544) :- log2(X541, s(X542), X543, X544).\nand substitutionX541 -> T312,\nT300 -> s(s(T312)),\nX542 -> s(s(s(0))),\nX543 -> s(s(s(0))),\nT301 -> T313,\nX544 -> T313" }, { "from": 587, "to": 591, "label": "EVAL-BACKTRACK" }, { "from": 588, "to": 4938, "label": "PARALLEL" }, { "from": 588, "to": 4939, "label": "PARALLEL" }, { "from": 590, "to": 595, "label": "CASE" }, { "from": 595, "to": 596, "label": "PARALLEL" }, { "from": 595, "to": 597, "label": "PARALLEL" }, { "from": 596, "to": 600, "label": "EVAL with clause\nlog2(s(s(X565)), X566, X567, X568) :- log2(X565, s(X566), X567, X568).\nand substitutionX565 -> T324,\nT312 -> s(s(T324)),\nX566 -> s(s(s(s(0)))),\nX567 -> s(s(s(0))),\nT313 -> T325,\nX568 -> T325" }, { "from": 596, "to": 601, "label": "EVAL-BACKTRACK" }, { "from": 597, "to": 4863, "label": "PARALLEL" }, { "from": 597, "to": 4864, "label": "PARALLEL" }, { "from": 600, "to": 602, "label": "CASE" }, { "from": 602, "to": 603, "label": "PARALLEL" }, { "from": 602, "to": 604, "label": "PARALLEL" }, { "from": 603, "to": 606, "label": "EVAL with clause\nlog2(s(s(X589)), X590, X591, X592) :- log2(X589, s(X590), X591, X592).\nand substitutionX589 -> T336,\nT324 -> s(s(T336)),\nX590 -> s(s(s(s(s(0))))),\nX591 -> s(s(s(0))),\nT325 -> T337,\nX592 -> T337" }, { "from": 603, "to": 607, "label": "EVAL-BACKTRACK" }, { "from": 604, "to": 4788, "label": "PARALLEL" }, { "from": 604, "to": 4789, "label": "PARALLEL" }, { "from": 606, "to": 610, "label": "CASE" }, { "from": 610, "to": 613, "label": "PARALLEL" }, { "from": 610, "to": 614, "label": "PARALLEL" }, { "from": 613, "to": 618, "label": "EVAL with clause\nlog2(s(s(X613)), X614, X615, X616) :- log2(X613, s(X614), X615, X616).\nand substitutionX613 -> T348,\nT336 -> s(s(T348)),\nX614 -> s(s(s(s(s(s(0)))))),\nX615 -> s(s(s(0))),\nT337 -> T349,\nX616 -> T349" }, { "from": 613, "to": 619, "label": "EVAL-BACKTRACK" }, { "from": 614, "to": 4713, "label": "PARALLEL" }, { "from": 614, "to": 4714, "label": "PARALLEL" }, { "from": 618, "to": 622, "label": "CASE" }, { "from": 622, "to": 626, "label": "PARALLEL" }, { "from": 622, "to": 627, "label": "PARALLEL" }, { "from": 626, "to": 630, "label": "EVAL with clause\nlog2(s(s(X637)), X638, X639, X640) :- log2(X637, s(X638), X639, X640).\nand substitutionX637 -> T360,\nT348 -> s(s(T360)),\nX638 -> s(s(s(s(s(s(s(0))))))),\nX639 -> s(s(s(0))),\nT349 -> T361,\nX640 -> T361" }, { "from": 626, "to": 631, "label": "EVAL-BACKTRACK" }, { "from": 627, "to": 4648, "label": "PARALLEL" }, { "from": 627, "to": 4649, "label": "PARALLEL" }, { "from": 630, "to": 633, "label": "GENERALIZATION\nT364 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT364 is ground" }, { "from": 633, "to": 637, "label": "CASE" }, { "from": 637, "to": 638, "label": "PARALLEL" }, { "from": 637, "to": 639, "label": "PARALLEL" }, { "from": 638, "to": 640, "label": "EVAL with clause\nlog2(s(s(X665)), X666, X667, X668) :- log2(X665, s(X666), X667, X668).\nand substitutionX665 -> T380,\nT360 -> s(s(T380)),\nT364 -> T381,\nX666 -> s(T381),\nX667 -> s(s(s(0))),\nT361 -> T382,\nX668 -> T382" }, { "from": 638, "to": 641, "label": "EVAL-BACKTRACK" }, { "from": 639, "to": 644, "label": "PARALLEL" }, { "from": 639, "to": 646, "label": "PARALLEL" }, { "from": 640, "to": 633, "label": "INSTANCE with matching:\nT360 -> T380\nT364 -> s(T381)\nT361 -> T382" }, { "from": 644, "to": 650, "label": "EVAL with clause\nlog2(X689, s(s(X690)), X691, X692) :- ','(small(X689), log2(X690, s(0), s(X691), X692)).\nand substitutionT360 -> T398,\nX689 -> T398,\nX690 -> T399,\nT364 -> s(T399),\nX691 -> s(s(s(0))),\nT361 -> T400,\nX692 -> T400" }, { "from": 644, "to": 651, "label": "EVAL-BACKTRACK" }, { "from": 646, "to": 4612, "label": "EVAL with clause\nlog2(X3435, X3436, X3437, X3437) :- ','(small(X3435), small(X3436)).\nand substitutionT360 -> T1721,\nX3435 -> T1721,\nT364 -> T1722,\nX3436 -> s(T1722),\nX3437 -> s(s(s(0))),\nT361 -> s(s(s(0)))" }, { "from": 646, "to": 4613, "label": "EVAL-BACKTRACK" }, { "from": 650, "to": 657, "label": "CASE" }, { "from": 657, "to": 658, "label": "PARALLEL" }, { "from": 657, "to": 659, "label": "PARALLEL" }, { "from": 658, "to": 660, "label": "EVAL with clause\nsmall(0).\nand substitutionT398 -> 0" }, { "from": 658, "to": 661, "label": "EVAL-BACKTRACK" }, { "from": 659, "to": 4601, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT398 -> s(0)" }, { "from": 659, "to": 4602, "label": "EVAL-BACKTRACK" }, { "from": 660, "to": 663, "label": "CASE" }, { "from": 663, "to": 666, "label": "PARALLEL" }, { "from": 663, "to": 667, "label": "PARALLEL" }, { "from": 666, "to": 671, "label": "EVAL with clause\nlog2(s(s(X717)), X718, X719, X720) :- log2(X717, s(X718), X719, X720).\nand substitutionX717 -> T413,\nT399 -> s(s(T413)),\nX718 -> s(0),\nX719 -> s(s(s(s(0)))),\nT400 -> T414,\nX720 -> T414" }, { "from": 666, "to": 672, "label": "EVAL-BACKTRACK" }, { "from": 667, "to": 4581, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 671, "to": 675, "label": "CASE" }, { "from": 675, "to": 678, "label": "PARALLEL" }, { "from": 675, "to": 679, "label": "PARALLEL" }, { "from": 678, "to": 680, "label": "EVAL with clause\nlog2(s(s(X741)), X742, X743, X744) :- log2(X741, s(X742), X743, X744).\nand substitutionX741 -> T425,\nT413 -> s(s(T425)),\nX742 -> s(s(0)),\nX743 -> s(s(s(s(0)))),\nT414 -> T426,\nX744 -> T426" }, { "from": 678, "to": 681, "label": "EVAL-BACKTRACK" }, { "from": 679, "to": 4477, "label": "PARALLEL" }, { "from": 679, "to": 4478, "label": "PARALLEL" }, { "from": 680, "to": 690, "label": "CASE" }, { "from": 690, "to": 691, "label": "PARALLEL" }, { "from": 690, "to": 692, "label": "PARALLEL" }, { "from": 691, "to": 697, "label": "EVAL with clause\nlog2(s(s(X765)), X766, X767, X768) :- log2(X765, s(X766), X767, X768).\nand substitutionX765 -> T437,\nT425 -> s(s(T437)),\nX766 -> s(s(s(0))),\nX767 -> s(s(s(s(0)))),\nT426 -> T438,\nX768 -> T438" }, { "from": 691, "to": 698, "label": "EVAL-BACKTRACK" }, { "from": 692, "to": 4402, "label": "PARALLEL" }, { "from": 692, "to": 4403, "label": "PARALLEL" }, { "from": 697, "to": 702, "label": "CASE" }, { "from": 702, "to": 706, "label": "PARALLEL" }, { "from": 702, "to": 707, "label": "PARALLEL" }, { "from": 706, "to": 713, "label": "EVAL with clause\nlog2(s(s(X789)), X790, X791, X792) :- log2(X789, s(X790), X791, X792).\nand substitutionX789 -> T449,\nT437 -> s(s(T449)),\nX790 -> s(s(s(s(0)))),\nX791 -> s(s(s(s(0)))),\nT438 -> T450,\nX792 -> T450" }, { "from": 706, "to": 714, "label": "EVAL-BACKTRACK" }, { "from": 707, "to": 4328, "label": "PARALLEL" }, { "from": 707, "to": 4329, "label": "PARALLEL" }, { "from": 713, "to": 719, "label": "CASE" }, { "from": 719, "to": 722, "label": "PARALLEL" }, { "from": 719, "to": 723, "label": "PARALLEL" }, { "from": 722, "to": 738, "label": "EVAL with clause\nlog2(s(s(X813)), X814, X815, X816) :- log2(X813, s(X814), X815, X816).\nand substitutionX813 -> T461,\nT449 -> s(s(T461)),\nX814 -> s(s(s(s(s(0))))),\nX815 -> s(s(s(s(0)))),\nT450 -> T462,\nX816 -> T462" }, { "from": 722, "to": 739, "label": "EVAL-BACKTRACK" }, { "from": 723, "to": 4253, "label": "PARALLEL" }, { "from": 723, "to": 4254, "label": "PARALLEL" }, { "from": 738, "to": 761, "label": "CASE" }, { "from": 761, "to": 767, "label": "PARALLEL" }, { "from": 761, "to": 768, "label": "PARALLEL" }, { "from": 767, "to": 774, "label": "EVAL with clause\nlog2(s(s(X837)), X838, X839, X840) :- log2(X837, s(X838), X839, X840).\nand substitutionX837 -> T473,\nT461 -> s(s(T473)),\nX838 -> s(s(s(s(s(s(0)))))),\nX839 -> s(s(s(s(0)))),\nT462 -> T474,\nX840 -> T474" }, { "from": 767, "to": 775, "label": "EVAL-BACKTRACK" }, { "from": 768, "to": 4180, "label": "PARALLEL" }, { "from": 768, "to": 4181, "label": "PARALLEL" }, { "from": 774, "to": 778, "label": "CASE" }, { "from": 778, "to": 788, "label": "PARALLEL" }, { "from": 778, "to": 789, "label": "PARALLEL" }, { "from": 788, "to": 796, "label": "EVAL with clause\nlog2(s(s(X861)), X862, X863, X864) :- log2(X861, s(X862), X863, X864).\nand substitutionX861 -> T485,\nT473 -> s(s(T485)),\nX862 -> s(s(s(s(s(s(s(0))))))),\nX863 -> s(s(s(s(0)))),\nT474 -> T486,\nX864 -> T486" }, { "from": 788, "to": 797, "label": "EVAL-BACKTRACK" }, { "from": 789, "to": 4105, "label": "PARALLEL" }, { "from": 789, "to": 4106, "label": "PARALLEL" }, { "from": 796, "to": 821, "label": "GENERALIZATION\nT489 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT489 is ground" }, { "from": 821, "to": 827, "label": "CASE" }, { "from": 827, "to": 830, "label": "PARALLEL" }, { "from": 827, "to": 831, "label": "PARALLEL" }, { "from": 830, "to": 833, "label": "EVAL with clause\nlog2(s(s(X889)), X890, X891, X892) :- log2(X889, s(X890), X891, X892).\nand substitutionX889 -> T505,\nT485 -> s(s(T505)),\nT489 -> T506,\nX890 -> s(T506),\nX891 -> s(s(s(s(0)))),\nT486 -> T507,\nX892 -> T507" }, { "from": 830, "to": 835, "label": "EVAL-BACKTRACK" }, { "from": 831, "to": 836, "label": "PARALLEL" }, { "from": 831, "to": 837, "label": "PARALLEL" }, { "from": 833, "to": 821, "label": "INSTANCE with matching:\nT485 -> T505\nT489 -> s(T506)\nT486 -> T507" }, { "from": 836, "to": 838, "label": "EVAL with clause\nlog2(X913, s(s(X914)), X915, X916) :- ','(small(X913), log2(X914, s(0), s(X915), X916)).\nand substitutionT485 -> T523,\nX913 -> T523,\nX914 -> T524,\nT489 -> s(T524),\nX915 -> s(s(s(s(0)))),\nT486 -> T525,\nX916 -> T525" }, { "from": 836, "to": 839, "label": "EVAL-BACKTRACK" }, { "from": 837, "to": 4084, "label": "EVAL with clause\nlog2(X3115, X3116, X3117, X3117) :- ','(small(X3115), small(X3116)).\nand substitutionT485 -> T1611,\nX3115 -> T1611,\nT489 -> T1612,\nX3116 -> s(T1612),\nX3117 -> s(s(s(s(0)))),\nT486 -> s(s(s(s(0))))" }, { "from": 837, "to": 4085, "label": "EVAL-BACKTRACK" }, { "from": 838, "to": 840, "label": "CASE" }, { "from": 840, "to": 841, "label": "PARALLEL" }, { "from": 840, "to": 842, "label": "PARALLEL" }, { "from": 841, "to": 843, "label": "EVAL with clause\nsmall(0).\nand substitutionT523 -> 0" }, { "from": 841, "to": 844, "label": "EVAL-BACKTRACK" }, { "from": 842, "to": 4050, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT523 -> s(0)" }, { "from": 842, "to": 4051, "label": "EVAL-BACKTRACK" }, { "from": 843, "to": 845, "label": "CASE" }, { "from": 845, "to": 846, "label": "PARALLEL" }, { "from": 845, "to": 847, "label": "PARALLEL" }, { "from": 846, "to": 848, "label": "EVAL with clause\nlog2(s(s(X941)), X942, X943, X944) :- log2(X941, s(X942), X943, X944).\nand substitutionX941 -> T538,\nT524 -> s(s(T538)),\nX942 -> s(0),\nX943 -> s(s(s(s(s(0))))),\nT525 -> T539,\nX944 -> T539" }, { "from": 846, "to": 849, "label": "EVAL-BACKTRACK" }, { "from": 847, "to": 4026, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 848, "to": 852, "label": "CASE" }, { "from": 852, "to": 859, "label": "PARALLEL" }, { "from": 852, "to": 860, "label": "PARALLEL" }, { "from": 859, "to": 878, "label": "EVAL with clause\nlog2(s(s(X965)), X966, X967, X968) :- log2(X965, s(X966), X967, X968).\nand substitutionX965 -> T550,\nT538 -> s(s(T550)),\nX966 -> s(s(0)),\nX967 -> s(s(s(s(s(0))))),\nT539 -> T551,\nX968 -> T551" }, { "from": 859, "to": 879, "label": "EVAL-BACKTRACK" }, { "from": 860, "to": 3963, "label": "PARALLEL" }, { "from": 860, "to": 3965, "label": "PARALLEL" }, { "from": 878, "to": 909, "label": "CASE" }, { "from": 909, "to": 912, "label": "PARALLEL" }, { "from": 909, "to": 913, "label": "PARALLEL" }, { "from": 912, "to": 914, "label": "EVAL with clause\nlog2(s(s(X989)), X990, X991, X992) :- log2(X989, s(X990), X991, X992).\nand substitutionX989 -> T562,\nT550 -> s(s(T562)),\nX990 -> s(s(s(0))),\nX991 -> s(s(s(s(s(0))))),\nT551 -> T563,\nX992 -> T563" }, { "from": 912, "to": 915, "label": "EVAL-BACKTRACK" }, { "from": 913, "to": 3880, "label": "PARALLEL" }, { "from": 913, "to": 3881, "label": "PARALLEL" }, { "from": 914, "to": 952, "label": "CASE" }, { "from": 952, "to": 973, "label": "PARALLEL" }, { "from": 952, "to": 974, "label": "PARALLEL" }, { "from": 973, "to": 980, "label": "EVAL with clause\nlog2(s(s(X1013)), X1014, X1015, X1016) :- log2(X1013, s(X1014), X1015, X1016).\nand substitutionX1013 -> T574,\nT562 -> s(s(T574)),\nX1014 -> s(s(s(s(0)))),\nX1015 -> s(s(s(s(s(0))))),\nT563 -> T575,\nX1016 -> T575" }, { "from": 973, "to": 981, "label": "EVAL-BACKTRACK" }, { "from": 974, "to": 3811, "label": "PARALLEL" }, { "from": 974, "to": 3813, "label": "PARALLEL" }, { "from": 980, "to": 987, "label": "CASE" }, { "from": 987, "to": 990, "label": "PARALLEL" }, { "from": 987, "to": 991, "label": "PARALLEL" }, { "from": 990, "to": 996, "label": "EVAL with clause\nlog2(s(s(X1037)), X1038, X1039, X1040) :- log2(X1037, s(X1038), X1039, X1040).\nand substitutionX1037 -> T586,\nT574 -> s(s(T586)),\nX1038 -> s(s(s(s(s(0))))),\nX1039 -> s(s(s(s(s(0))))),\nT575 -> T587,\nX1040 -> T587" }, { "from": 990, "to": 997, "label": "EVAL-BACKTRACK" }, { "from": 991, "to": 3734, "label": "PARALLEL" }, { "from": 991, "to": 3735, "label": "PARALLEL" }, { "from": 996, "to": 999, "label": "CASE" }, { "from": 999, "to": 1002, "label": "PARALLEL" }, { "from": 999, "to": 1003, "label": "PARALLEL" }, { "from": 1002, "to": 1006, "label": "EVAL with clause\nlog2(s(s(X1061)), X1062, X1063, X1064) :- log2(X1061, s(X1062), X1063, X1064).\nand substitutionX1061 -> T598,\nT586 -> s(s(T598)),\nX1062 -> s(s(s(s(s(s(0)))))),\nX1063 -> s(s(s(s(s(0))))),\nT587 -> T599,\nX1064 -> T599" }, { "from": 1002, "to": 1007, "label": "EVAL-BACKTRACK" }, { "from": 1003, "to": 3659, "label": "PARALLEL" }, { "from": 1003, "to": 3660, "label": "PARALLEL" }, { "from": 1006, "to": 1009, "label": "CASE" }, { "from": 1009, "to": 1012, "label": "PARALLEL" }, { "from": 1009, "to": 1013, "label": "PARALLEL" }, { "from": 1012, "to": 1016, "label": "EVAL with clause\nlog2(s(s(X1085)), X1086, X1087, X1088) :- log2(X1085, s(X1086), X1087, X1088).\nand substitutionX1085 -> T610,\nT598 -> s(s(T610)),\nX1086 -> s(s(s(s(s(s(s(0))))))),\nX1087 -> s(s(s(s(s(0))))),\nT599 -> T611,\nX1088 -> T611" }, { "from": 1012, "to": 1017, "label": "EVAL-BACKTRACK" }, { "from": 1013, "to": 3585, "label": "PARALLEL" }, { "from": 1013, "to": 3586, "label": "PARALLEL" }, { "from": 1016, "to": 1018, "label": "GENERALIZATION\nT614 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT614 is ground" }, { "from": 1018, "to": 1019, "label": "CASE" }, { "from": 1019, "to": 1027, "label": "PARALLEL" }, { "from": 1019, "to": 1028, "label": "PARALLEL" }, { "from": 1027, "to": 1029, "label": "EVAL with clause\nlog2(s(s(X1113)), X1114, X1115, X1116) :- log2(X1113, s(X1114), X1115, X1116).\nand substitutionX1113 -> T630,\nT610 -> s(s(T630)),\nT614 -> T631,\nX1114 -> s(T631),\nX1115 -> s(s(s(s(s(0))))),\nT611 -> T632,\nX1116 -> T632" }, { "from": 1027, "to": 1030, "label": "EVAL-BACKTRACK" }, { "from": 1028, "to": 1034, "label": "PARALLEL" }, { "from": 1028, "to": 1035, "label": "PARALLEL" }, { "from": 1029, "to": 1018, "label": "INSTANCE with matching:\nT610 -> T630\nT614 -> s(T631)\nT611 -> T632" }, { "from": 1034, "to": 1043, "label": "EVAL with clause\nlog2(X1137, s(s(X1138)), X1139, X1140) :- ','(small(X1137), log2(X1138, s(0), s(X1139), X1140)).\nand substitutionT610 -> T648,\nX1137 -> T648,\nX1138 -> T649,\nT614 -> s(T649),\nX1139 -> s(s(s(s(s(0))))),\nT611 -> T650,\nX1140 -> T650" }, { "from": 1034, "to": 1044, "label": "EVAL-BACKTRACK" }, { "from": 1035, "to": 3551, "label": "EVAL with clause\nlog2(X2795, X2796, X2797, X2797) :- ','(small(X2795), small(X2796)).\nand substitutionT610 -> T1501,\nX2795 -> T1501,\nT614 -> T1502,\nX2796 -> s(T1502),\nX2797 -> s(s(s(s(s(0))))),\nT611 -> s(s(s(s(s(0)))))" }, { "from": 1035, "to": 3552, "label": "EVAL-BACKTRACK" }, { "from": 1043, "to": 1046, "label": "CASE" }, { "from": 1046, "to": 1047, "label": "PARALLEL" }, { "from": 1046, "to": 1048, "label": "PARALLEL" }, { "from": 1047, "to": 1049, "label": "EVAL with clause\nsmall(0).\nand substitutionT648 -> 0" }, { "from": 1047, "to": 1050, "label": "EVAL-BACKTRACK" }, { "from": 1048, "to": 3545, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT648 -> s(0)" }, { "from": 1048, "to": 3546, "label": "EVAL-BACKTRACK" }, { "from": 1049, "to": 1052, "label": "CASE" }, { "from": 1052, "to": 1055, "label": "PARALLEL" }, { "from": 1052, "to": 1056, "label": "PARALLEL" }, { "from": 1055, "to": 1057, "label": "EVAL with clause\nlog2(s(s(X1165)), X1166, X1167, X1168) :- log2(X1165, s(X1166), X1167, X1168).\nand substitutionX1165 -> T663,\nT649 -> s(s(T663)),\nX1166 -> s(0),\nX1167 -> s(s(s(s(s(s(0)))))),\nT650 -> T664,\nX1168 -> T664" }, { "from": 1055, "to": 1058, "label": "EVAL-BACKTRACK" }, { "from": 1056, "to": 3526, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1057, "to": 1060, "label": "CASE" }, { "from": 1060, "to": 1061, "label": "PARALLEL" }, { "from": 1060, "to": 1062, "label": "PARALLEL" }, { "from": 1061, "to": 1072, "label": "EVAL with clause\nlog2(s(s(X1189)), X1190, X1191, X1192) :- log2(X1189, s(X1190), X1191, X1192).\nand substitutionX1189 -> T675,\nT663 -> s(s(T675)),\nX1190 -> s(s(0)),\nX1191 -> s(s(s(s(s(s(0)))))),\nT664 -> T676,\nX1192 -> T676" }, { "from": 1061, "to": 1073, "label": "EVAL-BACKTRACK" }, { "from": 1062, "to": 3470, "label": "PARALLEL" }, { "from": 1062, "to": 3471, "label": "PARALLEL" }, { "from": 1072, "to": 1076, "label": "CASE" }, { "from": 1076, "to": 1082, "label": "PARALLEL" }, { "from": 1076, "to": 1083, "label": "PARALLEL" }, { "from": 1082, "to": 1088, "label": "EVAL with clause\nlog2(s(s(X1213)), X1214, X1215, X1216) :- log2(X1213, s(X1214), X1215, X1216).\nand substitutionX1213 -> T687,\nT675 -> s(s(T687)),\nX1214 -> s(s(s(0))),\nX1215 -> s(s(s(s(s(s(0)))))),\nT676 -> T688,\nX1216 -> T688" }, { "from": 1082, "to": 1089, "label": "EVAL-BACKTRACK" }, { "from": 1083, "to": 3377, "label": "PARALLEL" }, { "from": 1083, "to": 3378, "label": "PARALLEL" }, { "from": 1088, "to": 1098, "label": "CASE" }, { "from": 1098, "to": 1101, "label": "PARALLEL" }, { "from": 1098, "to": 1102, "label": "PARALLEL" }, { "from": 1101, "to": 1103, "label": "EVAL with clause\nlog2(s(s(X1237)), X1238, X1239, X1240) :- log2(X1237, s(X1238), X1239, X1240).\nand substitutionX1237 -> T699,\nT687 -> s(s(T699)),\nX1238 -> s(s(s(s(0)))),\nX1239 -> s(s(s(s(s(s(0)))))),\nT688 -> T700,\nX1240 -> T700" }, { "from": 1101, "to": 1104, "label": "EVAL-BACKTRACK" }, { "from": 1102, "to": 3320, "label": "PARALLEL" }, { "from": 1102, "to": 3321, "label": "PARALLEL" }, { "from": 1103, "to": 1105, "label": "CASE" }, { "from": 1105, "to": 1106, "label": "PARALLEL" }, { "from": 1105, "to": 1107, "label": "PARALLEL" }, { "from": 1106, "to": 1108, "label": "EVAL with clause\nlog2(s(s(X1261)), X1262, X1263, X1264) :- log2(X1261, s(X1262), X1263, X1264).\nand substitutionX1261 -> T711,\nT699 -> s(s(T711)),\nX1262 -> s(s(s(s(s(0))))),\nX1263 -> s(s(s(s(s(s(0)))))),\nT700 -> T712,\nX1264 -> T712" }, { "from": 1106, "to": 1109, "label": "EVAL-BACKTRACK" }, { "from": 1107, "to": 3195, "label": "PARALLEL" }, { "from": 1107, "to": 3196, "label": "PARALLEL" }, { "from": 1108, "to": 1110, "label": "CASE" }, { "from": 1110, "to": 1111, "label": "PARALLEL" }, { "from": 1110, "to": 1112, "label": "PARALLEL" }, { "from": 1111, "to": 1113, "label": "EVAL with clause\nlog2(s(s(X1285)), X1286, X1287, X1288) :- log2(X1285, s(X1286), X1287, X1288).\nand substitutionX1285 -> T723,\nT711 -> s(s(T723)),\nX1286 -> s(s(s(s(s(s(0)))))),\nX1287 -> s(s(s(s(s(s(0)))))),\nT712 -> T724,\nX1288 -> T724" }, { "from": 1111, "to": 1114, "label": "EVAL-BACKTRACK" }, { "from": 1112, "to": 3086, "label": "PARALLEL" }, { "from": 1112, "to": 3087, "label": "PARALLEL" }, { "from": 1113, "to": 1115, "label": "CASE" }, { "from": 1115, "to": 1116, "label": "PARALLEL" }, { "from": 1115, "to": 1117, "label": "PARALLEL" }, { "from": 1116, "to": 1124, "label": "EVAL with clause\nlog2(s(s(X1309)), X1310, X1311, X1312) :- log2(X1309, s(X1310), X1311, X1312).\nand substitutionX1309 -> T735,\nT723 -> s(s(T735)),\nX1310 -> s(s(s(s(s(s(s(0))))))),\nX1311 -> s(s(s(s(s(s(0)))))),\nT724 -> T736,\nX1312 -> T736" }, { "from": 1116, "to": 1125, "label": "EVAL-BACKTRACK" }, { "from": 1117, "to": 3010, "label": "PARALLEL" }, { "from": 1117, "to": 3011, "label": "PARALLEL" }, { "from": 1124, "to": 1133, "label": "GENERALIZATION\nT739 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT739 is ground" }, { "from": 1133, "to": 1146, "label": "CASE" }, { "from": 1146, "to": 1158, "label": "PARALLEL" }, { "from": 1146, "to": 1162, "label": "PARALLEL" }, { "from": 1158, "to": 1174, "label": "EVAL with clause\nlog2(s(s(X1337)), X1338, X1339, X1340) :- log2(X1337, s(X1338), X1339, X1340).\nand substitutionX1337 -> T755,\nT735 -> s(s(T755)),\nT739 -> T756,\nX1338 -> s(T756),\nX1339 -> s(s(s(s(s(s(0)))))),\nT736 -> T757,\nX1340 -> T757" }, { "from": 1158, "to": 1175, "label": "EVAL-BACKTRACK" }, { "from": 1162, "to": 1190, "label": "PARALLEL" }, { "from": 1162, "to": 1191, "label": "PARALLEL" }, { "from": 1174, "to": 1133, "label": "INSTANCE with matching:\nT735 -> T755\nT739 -> s(T756)\nT736 -> T757" }, { "from": 1190, "to": 1194, "label": "EVAL with clause\nlog2(X1361, s(s(X1362)), X1363, X1364) :- ','(small(X1361), log2(X1362, s(0), s(X1363), X1364)).\nand substitutionT735 -> T773,\nX1361 -> T773,\nX1362 -> T774,\nT739 -> s(T774),\nX1363 -> s(s(s(s(s(s(0)))))),\nT736 -> T775,\nX1364 -> T775" }, { "from": 1190, "to": 1195, "label": "EVAL-BACKTRACK" }, { "from": 1191, "to": 2964, "label": "EVAL with clause\nlog2(X2475, X2476, X2477, X2477) :- ','(small(X2475), small(X2476)).\nand substitutionT735 -> T1391,\nX2475 -> T1391,\nT739 -> T1392,\nX2476 -> s(T1392),\nX2477 -> s(s(s(s(s(s(0)))))),\nT736 -> s(s(s(s(s(s(0))))))" }, { "from": 1191, "to": 2966, "label": "EVAL-BACKTRACK" }, { "from": 1194, "to": 1196, "label": "CASE" }, { "from": 1196, "to": 1197, "label": "PARALLEL" }, { "from": 1196, "to": 1198, "label": "PARALLEL" }, { "from": 1197, "to": 1199, "label": "EVAL with clause\nsmall(0).\nand substitutionT773 -> 0" }, { "from": 1197, "to": 1200, "label": "EVAL-BACKTRACK" }, { "from": 1198, "to": 2954, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT773 -> s(0)" }, { "from": 1198, "to": 2955, "label": "EVAL-BACKTRACK" }, { "from": 1199, "to": 1205, "label": "CASE" }, { "from": 1205, "to": 1213, "label": "PARALLEL" }, { "from": 1205, "to": 1214, "label": "PARALLEL" }, { "from": 1213, "to": 1218, "label": "EVAL with clause\nlog2(s(s(X1389)), X1390, X1391, X1392) :- log2(X1389, s(X1390), X1391, X1392).\nand substitutionX1389 -> T788,\nT774 -> s(s(T788)),\nX1390 -> s(0),\nX1391 -> s(s(s(s(s(s(s(0))))))),\nT775 -> T789,\nX1392 -> T789" }, { "from": 1213, "to": 1219, "label": "EVAL-BACKTRACK" }, { "from": 1214, "to": 2917, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1218, "to": 1223, "label": "CASE" }, { "from": 1223, "to": 1226, "label": "PARALLEL" }, { "from": 1223, "to": 1227, "label": "PARALLEL" }, { "from": 1226, "to": 1230, "label": "EVAL with clause\nlog2(s(s(X1413)), X1414, X1415, X1416) :- log2(X1413, s(X1414), X1415, X1416).\nand substitutionX1413 -> T800,\nT788 -> s(s(T800)),\nX1414 -> s(s(0)),\nX1415 -> s(s(s(s(s(s(s(0))))))),\nT789 -> T801,\nX1416 -> T801" }, { "from": 1226, "to": 1237, "label": "EVAL-BACKTRACK" }, { "from": 1227, "to": 2857, "label": "PARALLEL" }, { "from": 1227, "to": 2858, "label": "PARALLEL" }, { "from": 1230, "to": 1240, "label": "CASE" }, { "from": 1240, "to": 1243, "label": "PARALLEL" }, { "from": 1240, "to": 1244, "label": "PARALLEL" }, { "from": 1243, "to": 1247, "label": "EVAL with clause\nlog2(s(s(X1437)), X1438, X1439, X1440) :- log2(X1437, s(X1438), X1439, X1440).\nand substitutionX1437 -> T812,\nT800 -> s(s(T812)),\nX1438 -> s(s(s(0))),\nX1439 -> s(s(s(s(s(s(s(0))))))),\nT801 -> T813,\nX1440 -> T813" }, { "from": 1243, "to": 1248, "label": "EVAL-BACKTRACK" }, { "from": 1244, "to": 2755, "label": "PARALLEL" }, { "from": 1244, "to": 2756, "label": "PARALLEL" }, { "from": 1247, "to": 1254, "label": "CASE" }, { "from": 1254, "to": 1255, "label": "PARALLEL" }, { "from": 1254, "to": 1256, "label": "PARALLEL" }, { "from": 1255, "to": 1269, "label": "EVAL with clause\nlog2(s(s(X1461)), X1462, X1463, X1464) :- log2(X1461, s(X1462), X1463, X1464).\nand substitutionX1461 -> T824,\nT812 -> s(s(T824)),\nX1462 -> s(s(s(s(0)))),\nX1463 -> s(s(s(s(s(s(s(0))))))),\nT813 -> T825,\nX1464 -> T825" }, { "from": 1255, "to": 1270, "label": "EVAL-BACKTRACK" }, { "from": 1256, "to": 2693, "label": "PARALLEL" }, { "from": 1256, "to": 2694, "label": "PARALLEL" }, { "from": 1269, "to": 1271, "label": "CASE" }, { "from": 1271, "to": 1275, "label": "PARALLEL" }, { "from": 1271, "to": 1276, "label": "PARALLEL" }, { "from": 1275, "to": 1297, "label": "EVAL with clause\nlog2(s(s(X1485)), X1486, X1487, X1488) :- log2(X1485, s(X1486), X1487, X1488).\nand substitutionX1485 -> T836,\nT824 -> s(s(T836)),\nX1486 -> s(s(s(s(s(0))))),\nX1487 -> s(s(s(s(s(s(s(0))))))),\nT825 -> T837,\nX1488 -> T837" }, { "from": 1275, "to": 1298, "label": "EVAL-BACKTRACK" }, { "from": 1276, "to": 2573, "label": "PARALLEL" }, { "from": 1276, "to": 2574, "label": "PARALLEL" }, { "from": 1297, "to": 1299, "label": "CASE" }, { "from": 1299, "to": 1312, "label": "PARALLEL" }, { "from": 1299, "to": 1313, "label": "PARALLEL" }, { "from": 1312, "to": 1314, "label": "EVAL with clause\nlog2(s(s(X1509)), X1510, X1511, X1512) :- log2(X1509, s(X1510), X1511, X1512).\nand substitutionX1509 -> T848,\nT836 -> s(s(T848)),\nX1510 -> s(s(s(s(s(s(0)))))),\nX1511 -> s(s(s(s(s(s(s(0))))))),\nT837 -> T849,\nX1512 -> T849" }, { "from": 1312, "to": 1315, "label": "EVAL-BACKTRACK" }, { "from": 1313, "to": 2529, "label": "PARALLEL" }, { "from": 1313, "to": 2530, "label": "PARALLEL" }, { "from": 1314, "to": 1323, "label": "CASE" }, { "from": 1323, "to": 1325, "label": "PARALLEL" }, { "from": 1323, "to": 1326, "label": "PARALLEL" }, { "from": 1325, "to": 1329, "label": "EVAL with clause\nlog2(s(s(X1533)), X1534, X1535, X1536) :- log2(X1533, s(X1534), X1535, X1536).\nand substitutionX1533 -> T860,\nT848 -> s(s(T860)),\nX1534 -> s(s(s(s(s(s(s(0))))))),\nX1535 -> s(s(s(s(s(s(s(0))))))),\nT849 -> T861,\nX1536 -> T861" }, { "from": 1325, "to": 1330, "label": "EVAL-BACKTRACK" }, { "from": 1326, "to": 2421, "label": "PARALLEL" }, { "from": 1326, "to": 2422, "label": "PARALLEL" }, { "from": 1329, "to": 1334, "label": "GENERALIZATION\nT864 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT864 is ground" }, { "from": 1334, "to": 1337, "label": "CASE" }, { "from": 1337, "to": 1339, "label": "PARALLEL" }, { "from": 1337, "to": 1341, "label": "PARALLEL" }, { "from": 1339, "to": 1345, "label": "EVAL with clause\nlog2(s(s(X1561)), X1562, X1563, X1564) :- log2(X1561, s(X1562), X1563, X1564).\nand substitutionX1561 -> T880,\nT860 -> s(s(T880)),\nT864 -> T881,\nX1562 -> s(T881),\nX1563 -> s(s(s(s(s(s(s(0))))))),\nT861 -> T882,\nX1564 -> T882" }, { "from": 1339, "to": 1346, "label": "EVAL-BACKTRACK" }, { "from": 1341, "to": 1352, "label": "PARALLEL" }, { "from": 1341, "to": 1353, "label": "PARALLEL" }, { "from": 1345, "to": 1334, "label": "INSTANCE with matching:\nT860 -> T880\nT864 -> s(T881)\nT861 -> T882" }, { "from": 1352, "to": 1357, "label": "EVAL with clause\nlog2(X1585, s(s(X1586)), X1587, X1588) :- ','(small(X1585), log2(X1586, s(0), s(X1587), X1588)).\nand substitutionT860 -> T898,\nX1585 -> T898,\nX1586 -> T899,\nT864 -> s(T899),\nX1587 -> s(s(s(s(s(s(s(0))))))),\nT861 -> T900,\nX1588 -> T900" }, { "from": 1352, "to": 1358, "label": "EVAL-BACKTRACK" }, { "from": 1353, "to": 2392, "label": "EVAL with clause\nlog2(X2155, X2156, X2157, X2157) :- ','(small(X2155), small(X2156)).\nand substitutionT860 -> T1281,\nX2155 -> T1281,\nT864 -> T1282,\nX2156 -> s(T1282),\nX2157 -> s(s(s(s(s(s(s(0))))))),\nT861 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 1353, "to": 2393, "label": "EVAL-BACKTRACK" }, { "from": 1357, "to": 1361, "label": "CASE" }, { "from": 1361, "to": 1362, "label": "PARALLEL" }, { "from": 1361, "to": 1363, "label": "PARALLEL" }, { "from": 1362, "to": 1364, "label": "EVAL with clause\nsmall(0).\nand substitutionT898 -> 0" }, { "from": 1362, "to": 1365, "label": "EVAL-BACKTRACK" }, { "from": 1363, "to": 2373, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT898 -> s(0)" }, { "from": 1363, "to": 2374, "label": "EVAL-BACKTRACK" }, { "from": 1364, "to": 1368, "label": "GENERALIZATION\nT905 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT905 is ground" }, { "from": 1368, "to": 1369, "label": "CASE" }, { "from": 1369, "to": 1378, "label": "PARALLEL" }, { "from": 1369, "to": 1379, "label": "PARALLEL" }, { "from": 1378, "to": 1382, "label": "EVAL with clause\nlog2(s(s(X1617)), X1618, X1619, X1620) :- log2(X1617, s(X1618), X1619, X1620).\nand substitutionX1617 -> T921,\nT899 -> s(s(T921)),\nX1618 -> s(0),\nT905 -> T922,\nX1619 -> s(T922),\nT900 -> T923,\nX1620 -> T923" }, { "from": 1378, "to": 1383, "label": "EVAL-BACKTRACK" }, { "from": 1379, "to": 2353, "label": "BACKTRACK\nfor clause: log2(X, s(s(Half)), Acc, Y) :- ','(small(X), log2(Half, s(0), s(Acc), Y))because of non-unification" }, { "from": 1382, "to": 1384, "label": "CASE" }, { "from": 1384, "to": 1386, "label": "PARALLEL" }, { "from": 1384, "to": 1387, "label": "PARALLEL" }, { "from": 1386, "to": 1409, "label": "EVAL with clause\nlog2(s(s(X1641)), X1642, X1643, X1644) :- log2(X1641, s(X1642), X1643, X1644).\nand substitutionX1641 -> T939,\nT921 -> s(s(T939)),\nX1642 -> s(s(0)),\nT922 -> T940,\nX1643 -> s(T940),\nT923 -> T941,\nX1644 -> T941" }, { "from": 1386, "to": 1410, "label": "EVAL-BACKTRACK" }, { "from": 1387, "to": 2284, "label": "PARALLEL" }, { "from": 1387, "to": 2285, "label": "PARALLEL" }, { "from": 1409, "to": 1412, "label": "CASE" }, { "from": 1412, "to": 1414, "label": "PARALLEL" }, { "from": 1412, "to": 1415, "label": "PARALLEL" }, { "from": 1414, "to": 1417, "label": "EVAL with clause\nlog2(s(s(X1665)), X1666, X1667, X1668) :- log2(X1665, s(X1666), X1667, X1668).\nand substitutionX1665 -> T957,\nT939 -> s(s(T957)),\nX1666 -> s(s(s(0))),\nT940 -> T958,\nX1667 -> s(T958),\nT941 -> T959,\nX1668 -> T959" }, { "from": 1414, "to": 1418, "label": "EVAL-BACKTRACK" }, { "from": 1415, "to": 2251, "label": "PARALLEL" }, { "from": 1415, "to": 2252, "label": "PARALLEL" }, { "from": 1417, "to": 1420, "label": "CASE" }, { "from": 1420, "to": 1431, "label": "PARALLEL" }, { "from": 1420, "to": 1432, "label": "PARALLEL" }, { "from": 1431, "to": 1440, "label": "EVAL with clause\nlog2(s(s(X1689)), X1690, X1691, X1692) :- log2(X1689, s(X1690), X1691, X1692).\nand substitutionX1689 -> T975,\nT957 -> s(s(T975)),\nX1690 -> s(s(s(s(0)))),\nT958 -> T976,\nX1691 -> s(T976),\nT959 -> T977,\nX1692 -> T977" }, { "from": 1431, "to": 1441, "label": "EVAL-BACKTRACK" }, { "from": 1432, "to": 2083, "label": "PARALLEL" }, { "from": 1432, "to": 2084, "label": "PARALLEL" }, { "from": 1440, "to": 1452, "label": "CASE" }, { "from": 1452, "to": 1453, "label": "PARALLEL" }, { "from": 1452, "to": 1454, "label": "PARALLEL" }, { "from": 1453, "to": 1458, "label": "EVAL with clause\nlog2(s(s(X1713)), X1714, X1715, X1716) :- log2(X1713, s(X1714), X1715, X1716).\nand substitutionX1713 -> T993,\nT975 -> s(s(T993)),\nX1714 -> s(s(s(s(s(0))))),\nT976 -> T994,\nX1715 -> s(T994),\nT977 -> T995,\nX1716 -> T995" }, { "from": 1453, "to": 1459, "label": "EVAL-BACKTRACK" }, { "from": 1454, "to": 1904, "label": "PARALLEL" }, { "from": 1454, "to": 1905, "label": "PARALLEL" }, { "from": 1458, "to": 1462, "label": "CASE" }, { "from": 1462, "to": 1465, "label": "PARALLEL" }, { "from": 1462, "to": 1466, "label": "PARALLEL" }, { "from": 1465, "to": 1468, "label": "EVAL with clause\nlog2(s(s(X1737)), X1738, X1739, X1740) :- log2(X1737, s(X1738), X1739, X1740).\nand substitutionX1737 -> T1011,\nT993 -> s(s(T1011)),\nX1738 -> s(s(s(s(s(s(0)))))),\nT994 -> T1012,\nX1739 -> s(T1012),\nT995 -> T1013,\nX1740 -> T1013" }, { "from": 1465, "to": 1469, "label": "EVAL-BACKTRACK" }, { "from": 1466, "to": 1632, "label": "PARALLEL" }, { "from": 1466, "to": 1633, "label": "PARALLEL" }, { "from": 1468, "to": 1472, "label": "CASE" }, { "from": 1472, "to": 1475, "label": "PARALLEL" }, { "from": 1472, "to": 1476, "label": "PARALLEL" }, { "from": 1475, "to": 1480, "label": "EVAL with clause\nlog2(s(s(X1761)), X1762, X1763, X1764) :- log2(X1761, s(X1762), X1763, X1764).\nand substitutionX1761 -> T1029,\nT1011 -> s(s(T1029)),\nX1762 -> s(s(s(s(s(s(s(0))))))),\nT1012 -> T1030,\nX1763 -> s(T1030),\nT1013 -> T1031,\nX1764 -> T1031" }, { "from": 1475, "to": 1481, "label": "EVAL-BACKTRACK" }, { "from": 1476, "to": 1569, "label": "PARALLEL" }, { "from": 1476, "to": 1570, "label": "PARALLEL" }, { "from": 1480, "to": 1489, "label": "GENERALIZATION\nT1035 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT1035 is ground" }, { "from": 1489, "to": 1492, "label": "CASE" }, { "from": 1492, "to": 1495, "label": "PARALLEL" }, { "from": 1492, "to": 1496, "label": "PARALLEL" }, { "from": 1495, "to": 1500, "label": "EVAL with clause\nlog2(s(s(X1789)), X1790, X1791, X1792) :- log2(X1789, s(X1790), X1791, X1792).\nand substitutionX1789 -> T1056,\nT1029 -> s(s(T1056)),\nT1035 -> T1057,\nX1790 -> s(T1057),\nT1030 -> T1058,\nX1791 -> s(T1058),\nT1031 -> T1059,\nX1792 -> T1059" }, { "from": 1495, "to": 1501, "label": "EVAL-BACKTRACK" }, { "from": 1496, "to": 1521, "label": "PARALLEL" }, { "from": 1496, "to": 1522, "label": "PARALLEL" }, { "from": 1500, "to": 1489, "label": "INSTANCE with matching:\nT1029 -> T1056\nT1035 -> s(T1057)\nT1030 -> T1058\nT1031 -> T1059" }, { "from": 1521, "to": 1525, "label": "EVAL with clause\nlog2(X1813, s(s(X1814)), X1815, X1816) :- ','(small(X1813), log2(X1814, s(0), s(X1815), X1816)).\nand substitutionT1029 -> T1080,\nX1813 -> T1080,\nX1814 -> T1081,\nT1035 -> s(T1081),\nT1030 -> T1082,\nX1815 -> s(T1082),\nT1031 -> T1083,\nX1816 -> T1083" }, { "from": 1521, "to": 1526, "label": "EVAL-BACKTRACK" }, { "from": 1522, "to": 1542, "label": "EVAL with clause\nlog2(X1835, X1836, X1837, X1837) :- ','(small(X1835), small(X1836)).\nand substitutionT1029 -> T1099,\nX1835 -> T1099,\nT1035 -> T1100,\nX1836 -> s(T1100),\nT1030 -> T1101,\nX1837 -> s(T1101),\nT1031 -> s(T1101)" }, { "from": 1522, "to": 1543, "label": "EVAL-BACKTRACK" }, { "from": 1525, "to": 1530, "label": "CASE" }, { "from": 1530, "to": 1531, "label": "PARALLEL" }, { "from": 1530, "to": 1532, "label": "PARALLEL" }, { "from": 1531, "to": 1533, "label": "EVAL with clause\nsmall(0).\nand substitutionT1080 -> 0" }, { "from": 1531, "to": 1534, "label": "EVAL-BACKTRACK" }, { "from": 1532, "to": 1536, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1080 -> s(0)" }, { "from": 1532, "to": 1537, "label": "EVAL-BACKTRACK" }, { "from": 1533, "to": 1368, "label": "INSTANCE with matching:\nT899 -> T1081\nT905 -> s(T1082)\nT900 -> T1083" }, { "from": 1536, "to": 1368, "label": "INSTANCE with matching:\nT899 -> T1081\nT905 -> s(T1082)\nT900 -> T1083" }, { "from": 1542, "to": 1545, "label": "CASE" }, { "from": 1545, "to": 1546, "label": "PARALLEL" }, { "from": 1545, "to": 1548, "label": "PARALLEL" }, { "from": 1546, "to": 1549, "label": "EVAL with clause\nsmall(0).\nand substitutionT1099 -> 0" }, { "from": 1546, "to": 1550, "label": "EVAL-BACKTRACK" }, { "from": 1548, "to": 1558, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1099 -> s(0)" }, { "from": 1548, "to": 1559, "label": "EVAL-BACKTRACK" }, { "from": 1549, "to": 1551, "label": "CASE" }, { "from": 1551, "to": 1552, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1552, "to": 1555, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1100 -> 0" }, { "from": 1552, "to": 1556, "label": "EVAL-BACKTRACK" }, { "from": 1555, "to": 1557, "label": "SUCCESS" }, { "from": 1558, "to": 1560, "label": "CASE" }, { "from": 1560, "to": 1561, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1561, "to": 1562, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1100 -> 0" }, { "from": 1561, "to": 1563, "label": "EVAL-BACKTRACK" }, { "from": 1562, "to": 1564, "label": "SUCCESS" }, { "from": 1569, "to": 1590, "label": "ONLY EVAL with clause\nlog2(X1862, s(s(X1863)), X1864, X1865) :- ','(small(X1862), log2(X1863, s(0), s(X1864), X1865)).\nand substitutionT1011 -> T1118,\nX1862 -> T1118,\nX1863 -> s(s(s(s(s(0))))),\nT1012 -> T1119,\nX1864 -> s(T1119),\nT1013 -> T1120,\nX1865 -> T1120" }, { "from": 1570, "to": 1609, "label": "EVAL with clause\nlog2(X1884, X1885, X1886, X1886) :- ','(small(X1884), small(X1885)).\nand substitutionT1011 -> T1131,\nX1884 -> T1131,\nX1885 -> s(s(s(s(s(s(s(0))))))),\nT1012 -> T1132,\nX1886 -> s(T1132),\nT1013 -> s(T1132)" }, { "from": 1570, "to": 1610, "label": "EVAL-BACKTRACK" }, { "from": 1590, "to": 1594, "label": "CASE" }, { "from": 1594, "to": 1595, "label": "PARALLEL" }, { "from": 1594, "to": 1596, "label": "PARALLEL" }, { "from": 1595, "to": 1597, "label": "EVAL with clause\nsmall(0).\nand substitutionT1118 -> 0" }, { "from": 1595, "to": 1598, "label": "EVAL-BACKTRACK" }, { "from": 1596, "to": 1601, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1118 -> s(0)" }, { "from": 1596, "to": 1602, "label": "EVAL-BACKTRACK" }, { "from": 1597, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(s(0)))))\nT905 -> s(T1119)\nT900 -> T1120" }, { "from": 1601, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(s(0)))))\nT905 -> s(T1119)\nT900 -> T1120" }, { "from": 1609, "to": 1611, "label": "CASE" }, { "from": 1611, "to": 1612, "label": "PARALLEL" }, { "from": 1611, "to": 1613, "label": "PARALLEL" }, { "from": 1612, "to": 1614, "label": "EVAL with clause\nsmall(0).\nand substitutionT1131 -> 0" }, { "from": 1612, "to": 1615, "label": "EVAL-BACKTRACK" }, { "from": 1613, "to": 1619, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1131 -> s(0)" }, { "from": 1613, "to": 1620, "label": "EVAL-BACKTRACK" }, { "from": 1614, "to": 1616, "label": "CASE" }, { "from": 1616, "to": 1617, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1617, "to": 1618, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1619, "to": 1623, "label": "CASE" }, { "from": 1623, "to": 1624, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1624, "to": 1625, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1632, "to": 1675, "label": "ONLY EVAL with clause\nlog2(X1911, s(s(X1912)), X1913, X1914) :- ','(small(X1911), log2(X1912, s(0), s(X1913), X1914)).\nand substitutionT993 -> T1149,\nX1911 -> T1149,\nX1912 -> s(s(s(s(0)))),\nT994 -> T1150,\nX1913 -> s(T1150),\nT995 -> T1151,\nX1914 -> T1151" }, { "from": 1633, "to": 1823, "label": "EVAL with clause\nlog2(X1933, X1934, X1935, X1935) :- ','(small(X1933), small(X1934)).\nand substitutionT993 -> T1162,\nX1933 -> T1162,\nX1934 -> s(s(s(s(s(s(0)))))),\nT994 -> T1163,\nX1935 -> s(T1163),\nT995 -> s(T1163)" }, { "from": 1633, "to": 1824, "label": "EVAL-BACKTRACK" }, { "from": 1675, "to": 1676, "label": "CASE" }, { "from": 1676, "to": 1678, "label": "PARALLEL" }, { "from": 1676, "to": 1679, "label": "PARALLEL" }, { "from": 1678, "to": 1680, "label": "EVAL with clause\nsmall(0).\nand substitutionT1149 -> 0" }, { "from": 1678, "to": 1681, "label": "EVAL-BACKTRACK" }, { "from": 1679, "to": 1769, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1149 -> s(0)" }, { "from": 1679, "to": 1770, "label": "EVAL-BACKTRACK" }, { "from": 1680, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(0))))\nT905 -> s(T1150)\nT900 -> T1151" }, { "from": 1769, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(0))))\nT905 -> s(T1150)\nT900 -> T1151" }, { "from": 1823, "to": 1837, "label": "CASE" }, { "from": 1837, "to": 1838, "label": "PARALLEL" }, { "from": 1837, "to": 1839, "label": "PARALLEL" }, { "from": 1838, "to": 1840, "label": "EVAL with clause\nsmall(0).\nand substitutionT1162 -> 0" }, { "from": 1838, "to": 1841, "label": "EVAL-BACKTRACK" }, { "from": 1839, "to": 1845, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1162 -> s(0)" }, { "from": 1839, "to": 1846, "label": "EVAL-BACKTRACK" }, { "from": 1840, "to": 1842, "label": "CASE" }, { "from": 1842, "to": 1843, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1843, "to": 1844, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1845, "to": 1847, "label": "CASE" }, { "from": 1847, "to": 1848, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 1848, "to": 1849, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 1904, "to": 1954, "label": "ONLY EVAL with clause\nlog2(X1960, s(s(X1961)), X1962, X1963) :- ','(small(X1960), log2(X1961, s(0), s(X1962), X1963)).\nand substitutionT975 -> T1180,\nX1960 -> T1180,\nX1961 -> s(s(s(0))),\nT976 -> T1181,\nX1962 -> s(T1181),\nT977 -> T1182,\nX1963 -> T1182" }, { "from": 1905, "to": 2043, "label": "EVAL with clause\nlog2(X1982, X1983, X1984, X1984) :- ','(small(X1982), small(X1983)).\nand substitutionT975 -> T1193,\nX1982 -> T1193,\nX1983 -> s(s(s(s(s(0))))),\nT976 -> T1194,\nX1984 -> s(T1194),\nT977 -> s(T1194)" }, { "from": 1905, "to": 2044, "label": "EVAL-BACKTRACK" }, { "from": 1954, "to": 1957, "label": "CASE" }, { "from": 1957, "to": 1958, "label": "PARALLEL" }, { "from": 1957, "to": 1959, "label": "PARALLEL" }, { "from": 1958, "to": 1960, "label": "EVAL with clause\nsmall(0).\nand substitutionT1180 -> 0" }, { "from": 1958, "to": 1961, "label": "EVAL-BACKTRACK" }, { "from": 1959, "to": 1962, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1180 -> s(0)" }, { "from": 1959, "to": 1963, "label": "EVAL-BACKTRACK" }, { "from": 1960, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(0)))\nT905 -> s(T1181)\nT900 -> T1182" }, { "from": 1962, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(0)))\nT905 -> s(T1181)\nT900 -> T1182" }, { "from": 2043, "to": 2045, "label": "CASE" }, { "from": 2045, "to": 2046, "label": "PARALLEL" }, { "from": 2045, "to": 2047, "label": "PARALLEL" }, { "from": 2046, "to": 2048, "label": "EVAL with clause\nsmall(0).\nand substitutionT1193 -> 0" }, { "from": 2046, "to": 2049, "label": "EVAL-BACKTRACK" }, { "from": 2047, "to": 2053, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1193 -> s(0)" }, { "from": 2047, "to": 2054, "label": "EVAL-BACKTRACK" }, { "from": 2048, "to": 2050, "label": "CASE" }, { "from": 2050, "to": 2051, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2051, "to": 2052, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2053, "to": 2055, "label": "CASE" }, { "from": 2055, "to": 2056, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2056, "to": 2057, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2083, "to": 2171, "label": "ONLY EVAL with clause\nlog2(X2009, s(s(X2010)), X2011, X2012) :- ','(small(X2009), log2(X2010, s(0), s(X2011), X2012)).\nand substitutionT957 -> T1211,\nX2009 -> T1211,\nX2010 -> s(s(0)),\nT958 -> T1212,\nX2011 -> s(T1212),\nT959 -> T1213,\nX2012 -> T1213" }, { "from": 2084, "to": 2228, "label": "EVAL with clause\nlog2(X2031, X2032, X2033, X2033) :- ','(small(X2031), small(X2032)).\nand substitutionT957 -> T1224,\nX2031 -> T1224,\nX2032 -> s(s(s(s(0)))),\nT958 -> T1225,\nX2033 -> s(T1225),\nT959 -> s(T1225)" }, { "from": 2084, "to": 2229, "label": "EVAL-BACKTRACK" }, { "from": 2171, "to": 2172, "label": "CASE" }, { "from": 2172, "to": 2175, "label": "PARALLEL" }, { "from": 2172, "to": 2176, "label": "PARALLEL" }, { "from": 2175, "to": 2179, "label": "EVAL with clause\nsmall(0).\nand substitutionT1211 -> 0" }, { "from": 2175, "to": 2180, "label": "EVAL-BACKTRACK" }, { "from": 2176, "to": 2188, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1211 -> s(0)" }, { "from": 2176, "to": 2189, "label": "EVAL-BACKTRACK" }, { "from": 2179, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(0))\nT905 -> s(T1212)\nT900 -> T1213" }, { "from": 2188, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(0))\nT905 -> s(T1212)\nT900 -> T1213" }, { "from": 2228, "to": 2230, "label": "CASE" }, { "from": 2230, "to": 2231, "label": "PARALLEL" }, { "from": 2230, "to": 2232, "label": "PARALLEL" }, { "from": 2231, "to": 2233, "label": "EVAL with clause\nsmall(0).\nand substitutionT1224 -> 0" }, { "from": 2231, "to": 2234, "label": "EVAL-BACKTRACK" }, { "from": 2232, "to": 2238, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1224 -> s(0)" }, { "from": 2232, "to": 2239, "label": "EVAL-BACKTRACK" }, { "from": 2233, "to": 2235, "label": "CASE" }, { "from": 2235, "to": 2236, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2236, "to": 2237, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2238, "to": 2240, "label": "CASE" }, { "from": 2240, "to": 2241, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2241, "to": 2242, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2251, "to": 2255, "label": "ONLY EVAL with clause\nlog2(X2058, s(s(X2059)), X2060, X2061) :- ','(small(X2058), log2(X2059, s(0), s(X2060), X2061)).\nand substitutionT939 -> T1238,\nX2058 -> T1238,\nX2059 -> s(0),\nT940 -> T1239,\nX2060 -> s(T1239),\nT941 -> T1240,\nX2061 -> T1240" }, { "from": 2252, "to": 2269, "label": "EVAL with clause\nlog2(X2080, X2081, X2082, X2082) :- ','(small(X2080), small(X2081)).\nand substitutionT939 -> T1245,\nX2080 -> T1245,\nX2081 -> s(s(s(0))),\nT940 -> T1246,\nX2082 -> s(T1246),\nT941 -> s(T1246)" }, { "from": 2252, "to": 2270, "label": "EVAL-BACKTRACK" }, { "from": 2255, "to": 2260, "label": "CASE" }, { "from": 2260, "to": 2261, "label": "PARALLEL" }, { "from": 2260, "to": 2262, "label": "PARALLEL" }, { "from": 2261, "to": 2263, "label": "EVAL with clause\nsmall(0).\nand substitutionT1238 -> 0" }, { "from": 2261, "to": 2264, "label": "EVAL-BACKTRACK" }, { "from": 2262, "to": 2265, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1238 -> s(0)" }, { "from": 2262, "to": 2266, "label": "EVAL-BACKTRACK" }, { "from": 2263, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(0)\nT905 -> s(T1239)\nT900 -> T1240" }, { "from": 2265, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(0)\nT905 -> s(T1239)\nT900 -> T1240" }, { "from": 2269, "to": 2271, "label": "CASE" }, { "from": 2271, "to": 2272, "label": "PARALLEL" }, { "from": 2271, "to": 2273, "label": "PARALLEL" }, { "from": 2272, "to": 2274, "label": "EVAL with clause\nsmall(0).\nand substitutionT1245 -> 0" }, { "from": 2272, "to": 2275, "label": "EVAL-BACKTRACK" }, { "from": 2273, "to": 2279, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1245 -> s(0)" }, { "from": 2273, "to": 2280, "label": "EVAL-BACKTRACK" }, { "from": 2274, "to": 2276, "label": "CASE" }, { "from": 2276, "to": 2277, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2277, "to": 2278, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2279, "to": 2281, "label": "CASE" }, { "from": 2281, "to": 2282, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2282, "to": 2283, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2284, "to": 2286, "label": "ONLY EVAL with clause\nlog2(X2107, s(s(X2108)), X2109, X2110) :- ','(small(X2107), log2(X2108, s(0), s(X2109), X2110)).\nand substitutionT921 -> T1259,\nX2107 -> T1259,\nX2108 -> 0,\nT922 -> T1260,\nX2109 -> s(T1260),\nT923 -> T1261,\nX2110 -> T1261" }, { "from": 2285, "to": 2317, "label": "EVAL with clause\nlog2(X2129, X2130, X2131, X2131) :- ','(small(X2129), small(X2130)).\nand substitutionT921 -> T1266,\nX2129 -> T1266,\nX2130 -> s(s(0)),\nT922 -> T1267,\nX2131 -> s(T1267),\nT923 -> s(T1267)" }, { "from": 2285, "to": 2318, "label": "EVAL-BACKTRACK" }, { "from": 2286, "to": 2289, "label": "CASE" }, { "from": 2289, "to": 2290, "label": "PARALLEL" }, { "from": 2289, "to": 2291, "label": "PARALLEL" }, { "from": 2290, "to": 2292, "label": "EVAL with clause\nsmall(0).\nand substitutionT1259 -> 0" }, { "from": 2290, "to": 2293, "label": "EVAL-BACKTRACK" }, { "from": 2291, "to": 2294, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1259 -> s(0)" }, { "from": 2291, "to": 2295, "label": "EVAL-BACKTRACK" }, { "from": 2292, "to": 1368, "label": "INSTANCE with matching:\nT899 -> 0\nT905 -> s(T1260)\nT900 -> T1261" }, { "from": 2294, "to": 1368, "label": "INSTANCE with matching:\nT899 -> 0\nT905 -> s(T1260)\nT900 -> T1261" }, { "from": 2317, "to": 2319, "label": "CASE" }, { "from": 2319, "to": 2336, "label": "PARALLEL" }, { "from": 2319, "to": 2337, "label": "PARALLEL" }, { "from": 2336, "to": 2338, "label": "EVAL with clause\nsmall(0).\nand substitutionT1266 -> 0" }, { "from": 2336, "to": 2339, "label": "EVAL-BACKTRACK" }, { "from": 2337, "to": 2344, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1266 -> s(0)" }, { "from": 2337, "to": 2345, "label": "EVAL-BACKTRACK" }, { "from": 2338, "to": 2340, "label": "CASE" }, { "from": 2340, "to": 2341, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2341, "to": 2342, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2344, "to": 2348, "label": "CASE" }, { "from": 2348, "to": 2349, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2349, "to": 2350, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2353, "to": 2356, "label": "EVAL with clause\nlog2(X2142, X2143, X2144, X2144) :- ','(small(X2142), small(X2143)).\nand substitutionT899 -> T1273,\nX2142 -> T1273,\nX2143 -> s(0),\nT905 -> T1274,\nX2144 -> s(T1274),\nT900 -> s(T1274)" }, { "from": 2353, "to": 2357, "label": "EVAL-BACKTRACK" }, { "from": 2356, "to": 2358, "label": "CASE" }, { "from": 2358, "to": 2359, "label": "PARALLEL" }, { "from": 2358, "to": 2360, "label": "PARALLEL" }, { "from": 2359, "to": 2361, "label": "EVAL with clause\nsmall(0).\nand substitutionT1273 -> 0" }, { "from": 2359, "to": 2362, "label": "EVAL-BACKTRACK" }, { "from": 2360, "to": 2367, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1273 -> s(0)" }, { "from": 2360, "to": 2368, "label": "EVAL-BACKTRACK" }, { "from": 2361, "to": 2363, "label": "CASE" }, { "from": 2363, "to": 2364, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2364, "to": 2365, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2365, "to": 2366, "label": "SUCCESS" }, { "from": 2367, "to": 2369, "label": "CASE" }, { "from": 2369, "to": 2370, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2370, "to": 2371, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2371, "to": 2372, "label": "SUCCESS" }, { "from": 2373, "to": 1368, "label": "INSTANCE with matching:\nT905 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2392, "to": 2394, "label": "CASE" }, { "from": 2394, "to": 2395, "label": "PARALLEL" }, { "from": 2394, "to": 2396, "label": "PARALLEL" }, { "from": 2395, "to": 2397, "label": "EVAL with clause\nsmall(0).\nand substitutionT1281 -> 0" }, { "from": 2395, "to": 2398, "label": "EVAL-BACKTRACK" }, { "from": 2396, "to": 2404, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1281 -> s(0)" }, { "from": 2396, "to": 2405, "label": "EVAL-BACKTRACK" }, { "from": 2397, "to": 2399, "label": "CASE" }, { "from": 2399, "to": 2400, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2400, "to": 2401, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1282 -> 0" }, { "from": 2400, "to": 2402, "label": "EVAL-BACKTRACK" }, { "from": 2401, "to": 2403, "label": "SUCCESS" }, { "from": 2404, "to": 2407, "label": "CASE" }, { "from": 2407, "to": 2408, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2408, "to": 2409, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1282 -> 0" }, { "from": 2408, "to": 2410, "label": "EVAL-BACKTRACK" }, { "from": 2409, "to": 2411, "label": "SUCCESS" }, { "from": 2421, "to": 2493, "label": "ONLY EVAL with clause\nlog2(X2182, s(s(X2183)), X2184, X2185) :- ','(small(X2182), log2(X2183, s(0), s(X2184), X2185)).\nand substitutionT848 -> T1293,\nX2182 -> T1293,\nX2183 -> s(s(s(s(s(0))))),\nX2184 -> s(s(s(s(s(s(s(0))))))),\nT849 -> T1294,\nX2185 -> T1294" }, { "from": 2422, "to": 2507, "label": "EVAL with clause\nlog2(X2204, X2205, X2206, X2206) :- ','(small(X2204), small(X2205)).\nand substitutionT848 -> T1300,\nX2204 -> T1300,\nX2205 -> s(s(s(s(s(s(s(0))))))),\nX2206 -> s(s(s(s(s(s(s(0))))))),\nT849 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2422, "to": 2508, "label": "EVAL-BACKTRACK" }, { "from": 2493, "to": 2494, "label": "CASE" }, { "from": 2494, "to": 2495, "label": "PARALLEL" }, { "from": 2494, "to": 2496, "label": "PARALLEL" }, { "from": 2495, "to": 2497, "label": "EVAL with clause\nsmall(0).\nand substitutionT1293 -> 0" }, { "from": 2495, "to": 2498, "label": "EVAL-BACKTRACK" }, { "from": 2496, "to": 2505, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1293 -> s(0)" }, { "from": 2496, "to": 2506, "label": "EVAL-BACKTRACK" }, { "from": 2497, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(s(0)))))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1294" }, { "from": 2505, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(s(0)))))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1294" }, { "from": 2507, "to": 2509, "label": "CASE" }, { "from": 2509, "to": 2510, "label": "PARALLEL" }, { "from": 2509, "to": 2511, "label": "PARALLEL" }, { "from": 2510, "to": 2512, "label": "EVAL with clause\nsmall(0).\nand substitutionT1300 -> 0" }, { "from": 2510, "to": 2513, "label": "EVAL-BACKTRACK" }, { "from": 2511, "to": 2517, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1300 -> s(0)" }, { "from": 2511, "to": 2518, "label": "EVAL-BACKTRACK" }, { "from": 2512, "to": 2514, "label": "CASE" }, { "from": 2514, "to": 2515, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2515, "to": 2516, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2517, "to": 2519, "label": "CASE" }, { "from": 2519, "to": 2520, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2520, "to": 2521, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2529, "to": 2546, "label": "ONLY EVAL with clause\nlog2(X2231, s(s(X2232)), X2233, X2234) :- ','(small(X2231), log2(X2232, s(0), s(X2233), X2234)).\nand substitutionT836 -> T1311,\nX2231 -> T1311,\nX2232 -> s(s(s(s(0)))),\nX2233 -> s(s(s(s(s(s(s(0))))))),\nT837 -> T1312,\nX2234 -> T1312" }, { "from": 2530, "to": 2554, "label": "EVAL with clause\nlog2(X2253, X2254, X2255, X2255) :- ','(small(X2253), small(X2254)).\nand substitutionT836 -> T1318,\nX2253 -> T1318,\nX2254 -> s(s(s(s(s(s(0)))))),\nX2255 -> s(s(s(s(s(s(s(0))))))),\nT837 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2530, "to": 2555, "label": "EVAL-BACKTRACK" }, { "from": 2546, "to": 2547, "label": "CASE" }, { "from": 2547, "to": 2548, "label": "PARALLEL" }, { "from": 2547, "to": 2549, "label": "PARALLEL" }, { "from": 2548, "to": 2550, "label": "EVAL with clause\nsmall(0).\nand substitutionT1311 -> 0" }, { "from": 2548, "to": 2551, "label": "EVAL-BACKTRACK" }, { "from": 2549, "to": 2552, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1311 -> s(0)" }, { "from": 2549, "to": 2553, "label": "EVAL-BACKTRACK" }, { "from": 2550, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(0))))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1312" }, { "from": 2552, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(s(0))))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1312" }, { "from": 2554, "to": 2556, "label": "CASE" }, { "from": 2556, "to": 2557, "label": "PARALLEL" }, { "from": 2556, "to": 2558, "label": "PARALLEL" }, { "from": 2557, "to": 2559, "label": "EVAL with clause\nsmall(0).\nand substitutionT1318 -> 0" }, { "from": 2557, "to": 2560, "label": "EVAL-BACKTRACK" }, { "from": 2558, "to": 2564, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1318 -> s(0)" }, { "from": 2558, "to": 2565, "label": "EVAL-BACKTRACK" }, { "from": 2559, "to": 2561, "label": "CASE" }, { "from": 2561, "to": 2562, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2562, "to": 2563, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2564, "to": 2566, "label": "CASE" }, { "from": 2566, "to": 2567, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2567, "to": 2568, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2573, "to": 2629, "label": "ONLY EVAL with clause\nlog2(X2280, s(s(X2281)), X2282, X2283) :- ','(small(X2280), log2(X2281, s(0), s(X2282), X2283)).\nand substitutionT824 -> T1329,\nX2280 -> T1329,\nX2281 -> s(s(s(0))),\nX2282 -> s(s(s(s(s(s(s(0))))))),\nT825 -> T1330,\nX2283 -> T1330" }, { "from": 2574, "to": 2663, "label": "EVAL with clause\nlog2(X2302, X2303, X2304, X2304) :- ','(small(X2302), small(X2303)).\nand substitutionT824 -> T1336,\nX2302 -> T1336,\nX2303 -> s(s(s(s(s(0))))),\nX2304 -> s(s(s(s(s(s(s(0))))))),\nT825 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2574, "to": 2664, "label": "EVAL-BACKTRACK" }, { "from": 2629, "to": 2636, "label": "CASE" }, { "from": 2636, "to": 2637, "label": "PARALLEL" }, { "from": 2636, "to": 2638, "label": "PARALLEL" }, { "from": 2637, "to": 2639, "label": "EVAL with clause\nsmall(0).\nand substitutionT1329 -> 0" }, { "from": 2637, "to": 2640, "label": "EVAL-BACKTRACK" }, { "from": 2638, "to": 2641, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1329 -> s(0)" }, { "from": 2638, "to": 2642, "label": "EVAL-BACKTRACK" }, { "from": 2639, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(0)))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1330" }, { "from": 2641, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(s(0)))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1330" }, { "from": 2663, "to": 2665, "label": "CASE" }, { "from": 2665, "to": 2666, "label": "PARALLEL" }, { "from": 2665, "to": 2667, "label": "PARALLEL" }, { "from": 2666, "to": 2668, "label": "EVAL with clause\nsmall(0).\nand substitutionT1336 -> 0" }, { "from": 2666, "to": 2669, "label": "EVAL-BACKTRACK" }, { "from": 2667, "to": 2673, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1336 -> s(0)" }, { "from": 2667, "to": 2674, "label": "EVAL-BACKTRACK" }, { "from": 2668, "to": 2670, "label": "CASE" }, { "from": 2670, "to": 2671, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2671, "to": 2672, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2673, "to": 2675, "label": "CASE" }, { "from": 2675, "to": 2676, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2676, "to": 2677, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2693, "to": 2700, "label": "ONLY EVAL with clause\nlog2(X2329, s(s(X2330)), X2331, X2332) :- ','(small(X2329), log2(X2330, s(0), s(X2331), X2332)).\nand substitutionT812 -> T1347,\nX2329 -> T1347,\nX2330 -> s(s(0)),\nX2331 -> s(s(s(s(s(s(s(0))))))),\nT813 -> T1348,\nX2332 -> T1348" }, { "from": 2694, "to": 2740, "label": "EVAL with clause\nlog2(X2351, X2352, X2353, X2353) :- ','(small(X2351), small(X2352)).\nand substitutionT812 -> T1354,\nX2351 -> T1354,\nX2352 -> s(s(s(s(0)))),\nX2353 -> s(s(s(s(s(s(s(0))))))),\nT813 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2694, "to": 2741, "label": "EVAL-BACKTRACK" }, { "from": 2700, "to": 2718, "label": "CASE" }, { "from": 2718, "to": 2719, "label": "PARALLEL" }, { "from": 2718, "to": 2720, "label": "PARALLEL" }, { "from": 2719, "to": 2721, "label": "EVAL with clause\nsmall(0).\nand substitutionT1347 -> 0" }, { "from": 2719, "to": 2722, "label": "EVAL-BACKTRACK" }, { "from": 2720, "to": 2723, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1347 -> s(0)" }, { "from": 2720, "to": 2724, "label": "EVAL-BACKTRACK" }, { "from": 2721, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(0))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1348" }, { "from": 2723, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(s(0))\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1348" }, { "from": 2740, "to": 2742, "label": "CASE" }, { "from": 2742, "to": 2743, "label": "PARALLEL" }, { "from": 2742, "to": 2744, "label": "PARALLEL" }, { "from": 2743, "to": 2745, "label": "EVAL with clause\nsmall(0).\nand substitutionT1354 -> 0" }, { "from": 2743, "to": 2746, "label": "EVAL-BACKTRACK" }, { "from": 2744, "to": 2750, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1354 -> s(0)" }, { "from": 2744, "to": 2751, "label": "EVAL-BACKTRACK" }, { "from": 2745, "to": 2747, "label": "CASE" }, { "from": 2747, "to": 2748, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2748, "to": 2749, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2750, "to": 2752, "label": "CASE" }, { "from": 2752, "to": 2753, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2753, "to": 2754, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2755, "to": 2782, "label": "ONLY EVAL with clause\nlog2(X2378, s(s(X2379)), X2380, X2381) :- ','(small(X2378), log2(X2379, s(0), s(X2380), X2381)).\nand substitutionT800 -> T1363,\nX2378 -> T1363,\nX2379 -> s(0),\nX2380 -> s(s(s(s(s(s(s(0))))))),\nT801 -> T1364,\nX2381 -> T1364" }, { "from": 2756, "to": 2810, "label": "EVAL with clause\nlog2(X2400, X2401, X2402, X2402) :- ','(small(X2400), small(X2401)).\nand substitutionT800 -> T1367,\nX2400 -> T1367,\nX2401 -> s(s(s(0))),\nX2402 -> s(s(s(s(s(s(s(0))))))),\nT801 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2756, "to": 2811, "label": "EVAL-BACKTRACK" }, { "from": 2782, "to": 2783, "label": "CASE" }, { "from": 2783, "to": 2784, "label": "PARALLEL" }, { "from": 2783, "to": 2785, "label": "PARALLEL" }, { "from": 2784, "to": 2786, "label": "EVAL with clause\nsmall(0).\nand substitutionT1363 -> 0" }, { "from": 2784, "to": 2787, "label": "EVAL-BACKTRACK" }, { "from": 2785, "to": 2808, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1363 -> s(0)" }, { "from": 2785, "to": 2809, "label": "EVAL-BACKTRACK" }, { "from": 2786, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(0)\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1364" }, { "from": 2808, "to": 1368, "label": "INSTANCE with matching:\nT899 -> s(0)\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1364" }, { "from": 2810, "to": 2812, "label": "CASE" }, { "from": 2812, "to": 2813, "label": "PARALLEL" }, { "from": 2812, "to": 2814, "label": "PARALLEL" }, { "from": 2813, "to": 2815, "label": "EVAL with clause\nsmall(0).\nand substitutionT1367 -> 0" }, { "from": 2813, "to": 2816, "label": "EVAL-BACKTRACK" }, { "from": 2814, "to": 2820, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1367 -> s(0)" }, { "from": 2814, "to": 2821, "label": "EVAL-BACKTRACK" }, { "from": 2815, "to": 2817, "label": "CASE" }, { "from": 2817, "to": 2818, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2818, "to": 2819, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2820, "to": 2822, "label": "CASE" }, { "from": 2822, "to": 2823, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2823, "to": 2824, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2857, "to": 2861, "label": "ONLY EVAL with clause\nlog2(X2427, s(s(X2428)), X2429, X2430) :- ','(small(X2427), log2(X2428, s(0), s(X2429), X2430)).\nand substitutionT788 -> T1376,\nX2427 -> T1376,\nX2428 -> 0,\nX2429 -> s(s(s(s(s(s(s(0))))))),\nT789 -> T1377,\nX2430 -> T1377" }, { "from": 2858, "to": 2896, "label": "EVAL with clause\nlog2(X2449, X2450, X2451, X2451) :- ','(small(X2449), small(X2450)).\nand substitutionT788 -> T1380,\nX2449 -> T1380,\nX2450 -> s(s(0)),\nX2451 -> s(s(s(s(s(s(s(0))))))),\nT789 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2858, "to": 2897, "label": "EVAL-BACKTRACK" }, { "from": 2861, "to": 2862, "label": "CASE" }, { "from": 2862, "to": 2864, "label": "PARALLEL" }, { "from": 2862, "to": 2865, "label": "PARALLEL" }, { "from": 2864, "to": 2866, "label": "EVAL with clause\nsmall(0).\nand substitutionT1376 -> 0" }, { "from": 2864, "to": 2867, "label": "EVAL-BACKTRACK" }, { "from": 2865, "to": 2873, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1376 -> s(0)" }, { "from": 2865, "to": 2874, "label": "EVAL-BACKTRACK" }, { "from": 2866, "to": 1368, "label": "INSTANCE with matching:\nT899 -> 0\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1377" }, { "from": 2873, "to": 1368, "label": "INSTANCE with matching:\nT899 -> 0\nT905 -> s(s(s(s(s(s(s(0)))))))\nT900 -> T1377" }, { "from": 2896, "to": 2898, "label": "CASE" }, { "from": 2898, "to": 2899, "label": "PARALLEL" }, { "from": 2898, "to": 2900, "label": "PARALLEL" }, { "from": 2899, "to": 2901, "label": "EVAL with clause\nsmall(0).\nand substitutionT1380 -> 0" }, { "from": 2899, "to": 2902, "label": "EVAL-BACKTRACK" }, { "from": 2900, "to": 2906, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1380 -> s(0)" }, { "from": 2900, "to": 2907, "label": "EVAL-BACKTRACK" }, { "from": 2901, "to": 2903, "label": "CASE" }, { "from": 2903, "to": 2904, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2904, "to": 2905, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2906, "to": 2908, "label": "CASE" }, { "from": 2908, "to": 2910, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2910, "to": 2914, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 2917, "to": 2937, "label": "EVAL with clause\nlog2(X2462, X2463, X2464, X2464) :- ','(small(X2462), small(X2463)).\nand substitutionT774 -> T1384,\nX2462 -> T1384,\nX2463 -> s(0),\nX2464 -> s(s(s(s(s(s(s(0))))))),\nT775 -> s(s(s(s(s(s(s(0)))))))" }, { "from": 2917, "to": 2938, "label": "EVAL-BACKTRACK" }, { "from": 2937, "to": 2939, "label": "CASE" }, { "from": 2939, "to": 2940, "label": "PARALLEL" }, { "from": 2939, "to": 2941, "label": "PARALLEL" }, { "from": 2940, "to": 2942, "label": "EVAL with clause\nsmall(0).\nand substitutionT1384 -> 0" }, { "from": 2940, "to": 2943, "label": "EVAL-BACKTRACK" }, { "from": 2941, "to": 2948, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1384 -> s(0)" }, { "from": 2941, "to": 2949, "label": "EVAL-BACKTRACK" }, { "from": 2942, "to": 2944, "label": "CASE" }, { "from": 2944, "to": 2945, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2945, "to": 2946, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2946, "to": 2947, "label": "SUCCESS" }, { "from": 2948, "to": 2950, "label": "CASE" }, { "from": 2950, "to": 2951, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2951, "to": 2952, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 2952, "to": 2953, "label": "SUCCESS" }, { "from": 2954, "to": 1199, "label": "INSTANCE" }, { "from": 2964, "to": 2967, "label": "CASE" }, { "from": 2967, "to": 2968, "label": "PARALLEL" }, { "from": 2967, "to": 2969, "label": "PARALLEL" }, { "from": 2968, "to": 2970, "label": "EVAL with clause\nsmall(0).\nand substitutionT1391 -> 0" }, { "from": 2968, "to": 2971, "label": "EVAL-BACKTRACK" }, { "from": 2969, "to": 2977, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1391 -> s(0)" }, { "from": 2969, "to": 2978, "label": "EVAL-BACKTRACK" }, { "from": 2970, "to": 2972, "label": "CASE" }, { "from": 2972, "to": 2973, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2973, "to": 2974, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1392 -> 0" }, { "from": 2973, "to": 2975, "label": "EVAL-BACKTRACK" }, { "from": 2974, "to": 2976, "label": "SUCCESS" }, { "from": 2977, "to": 2979, "label": "CASE" }, { "from": 2979, "to": 2980, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 2980, "to": 2981, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1392 -> 0" }, { "from": 2980, "to": 2982, "label": "EVAL-BACKTRACK" }, { "from": 2981, "to": 2983, "label": "SUCCESS" }, { "from": 3010, "to": 3030, "label": "ONLY EVAL with clause\nlog2(X2502, s(s(X2503)), X2504, X2505) :- ','(small(X2502), log2(X2503, s(0), s(X2504), X2505)).\nand substitutionT723 -> T1403,\nX2502 -> T1403,\nX2503 -> s(s(s(s(s(0))))),\nX2504 -> s(s(s(s(s(s(0)))))),\nT724 -> T1404,\nX2505 -> T1404" }, { "from": 3011, "to": 3071, "label": "EVAL with clause\nlog2(X2524, X2525, X2526, X2526) :- ','(small(X2524), small(X2525)).\nand substitutionT723 -> T1410,\nX2524 -> T1410,\nX2525 -> s(s(s(s(s(s(s(0))))))),\nX2526 -> s(s(s(s(s(s(0)))))),\nT724 -> s(s(s(s(s(s(0))))))" }, { "from": 3011, "to": 3072, "label": "EVAL-BACKTRACK" }, { "from": 3030, "to": 3031, "label": "CASE" }, { "from": 3031, "to": 3032, "label": "PARALLEL" }, { "from": 3031, "to": 3033, "label": "PARALLEL" }, { "from": 3032, "to": 3034, "label": "EVAL with clause\nsmall(0).\nand substitutionT1403 -> 0" }, { "from": 3032, "to": 3035, "label": "EVAL-BACKTRACK" }, { "from": 3033, "to": 3050, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1403 -> s(0)" }, { "from": 3033, "to": 3051, "label": "EVAL-BACKTRACK" }, { "from": 3034, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(s(s(0)))))\nT775 -> T1404" }, { "from": 3050, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(s(s(0)))))\nT775 -> T1404" }, { "from": 3071, "to": 3073, "label": "CASE" }, { "from": 3073, "to": 3074, "label": "PARALLEL" }, { "from": 3073, "to": 3075, "label": "PARALLEL" }, { "from": 3074, "to": 3076, "label": "EVAL with clause\nsmall(0).\nand substitutionT1410 -> 0" }, { "from": 3074, "to": 3077, "label": "EVAL-BACKTRACK" }, { "from": 3075, "to": 3081, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1410 -> s(0)" }, { "from": 3075, "to": 3082, "label": "EVAL-BACKTRACK" }, { "from": 3076, "to": 3078, "label": "CASE" }, { "from": 3078, "to": 3079, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3079, "to": 3080, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3081, "to": 3083, "label": "CASE" }, { "from": 3083, "to": 3084, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3084, "to": 3085, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3086, "to": 3119, "label": "ONLY EVAL with clause\nlog2(X2551, s(s(X2552)), X2553, X2554) :- ','(small(X2551), log2(X2552, s(0), s(X2553), X2554)).\nand substitutionT711 -> T1421,\nX2551 -> T1421,\nX2552 -> s(s(s(s(0)))),\nX2553 -> s(s(s(s(s(s(0)))))),\nT712 -> T1422,\nX2554 -> T1422" }, { "from": 3087, "to": 3171, "label": "EVAL with clause\nlog2(X2573, X2574, X2575, X2575) :- ','(small(X2573), small(X2574)).\nand substitutionT711 -> T1428,\nX2573 -> T1428,\nX2574 -> s(s(s(s(s(s(0)))))),\nX2575 -> s(s(s(s(s(s(0)))))),\nT712 -> s(s(s(s(s(s(0))))))" }, { "from": 3087, "to": 3172, "label": "EVAL-BACKTRACK" }, { "from": 3119, "to": 3120, "label": "CASE" }, { "from": 3120, "to": 3121, "label": "PARALLEL" }, { "from": 3120, "to": 3122, "label": "PARALLEL" }, { "from": 3121, "to": 3125, "label": "EVAL with clause\nsmall(0).\nand substitutionT1421 -> 0" }, { "from": 3121, "to": 3126, "label": "EVAL-BACKTRACK" }, { "from": 3122, "to": 3127, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1421 -> s(0)" }, { "from": 3122, "to": 3128, "label": "EVAL-BACKTRACK" }, { "from": 3125, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(s(0))))\nT775 -> T1422" }, { "from": 3127, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(s(0))))\nT775 -> T1422" }, { "from": 3171, "to": 3173, "label": "CASE" }, { "from": 3173, "to": 3174, "label": "PARALLEL" }, { "from": 3173, "to": 3175, "label": "PARALLEL" }, { "from": 3174, "to": 3176, "label": "EVAL with clause\nsmall(0).\nand substitutionT1428 -> 0" }, { "from": 3174, "to": 3177, "label": "EVAL-BACKTRACK" }, { "from": 3175, "to": 3181, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1428 -> s(0)" }, { "from": 3175, "to": 3182, "label": "EVAL-BACKTRACK" }, { "from": 3176, "to": 3178, "label": "CASE" }, { "from": 3178, "to": 3179, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3179, "to": 3180, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3181, "to": 3183, "label": "CASE" }, { "from": 3183, "to": 3184, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3184, "to": 3185, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3195, "to": 3237, "label": "ONLY EVAL with clause\nlog2(X2600, s(s(X2601)), X2602, X2603) :- ','(small(X2600), log2(X2601, s(0), s(X2602), X2603)).\nand substitutionT699 -> T1439,\nX2600 -> T1439,\nX2601 -> s(s(s(0))),\nX2602 -> s(s(s(s(s(s(0)))))),\nT700 -> T1440,\nX2603 -> T1440" }, { "from": 3196, "to": 3265, "label": "EVAL with clause\nlog2(X2622, X2623, X2624, X2624) :- ','(small(X2622), small(X2623)).\nand substitutionT699 -> T1446,\nX2622 -> T1446,\nX2623 -> s(s(s(s(s(0))))),\nX2624 -> s(s(s(s(s(s(0)))))),\nT700 -> s(s(s(s(s(s(0))))))" }, { "from": 3196, "to": 3266, "label": "EVAL-BACKTRACK" }, { "from": 3237, "to": 3238, "label": "CASE" }, { "from": 3238, "to": 3239, "label": "PARALLEL" }, { "from": 3238, "to": 3240, "label": "PARALLEL" }, { "from": 3239, "to": 3241, "label": "EVAL with clause\nsmall(0).\nand substitutionT1439 -> 0" }, { "from": 3239, "to": 3242, "label": "EVAL-BACKTRACK" }, { "from": 3240, "to": 3244, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1439 -> s(0)" }, { "from": 3240, "to": 3245, "label": "EVAL-BACKTRACK" }, { "from": 3241, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(0)))\nT775 -> T1440" }, { "from": 3244, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(s(0)))\nT775 -> T1440" }, { "from": 3265, "to": 3267, "label": "CASE" }, { "from": 3267, "to": 3268, "label": "PARALLEL" }, { "from": 3267, "to": 3269, "label": "PARALLEL" }, { "from": 3268, "to": 3270, "label": "EVAL with clause\nsmall(0).\nand substitutionT1446 -> 0" }, { "from": 3268, "to": 3271, "label": "EVAL-BACKTRACK" }, { "from": 3269, "to": 3275, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1446 -> s(0)" }, { "from": 3269, "to": 3276, "label": "EVAL-BACKTRACK" }, { "from": 3270, "to": 3272, "label": "CASE" }, { "from": 3272, "to": 3273, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3273, "to": 3274, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3275, "to": 3277, "label": "CASE" }, { "from": 3277, "to": 3278, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3278, "to": 3279, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3320, "to": 3324, "label": "ONLY EVAL with clause\nlog2(X2649, s(s(X2650)), X2651, X2652) :- ','(small(X2649), log2(X2650, s(0), s(X2651), X2652)).\nand substitutionT687 -> T1457,\nX2649 -> T1457,\nX2650 -> s(s(0)),\nX2651 -> s(s(s(s(s(s(0)))))),\nT688 -> T1458,\nX2652 -> T1458" }, { "from": 3321, "to": 3360, "label": "EVAL with clause\nlog2(X2671, X2672, X2673, X2673) :- ','(small(X2671), small(X2672)).\nand substitutionT687 -> T1464,\nX2671 -> T1464,\nX2672 -> s(s(s(s(0)))),\nX2673 -> s(s(s(s(s(s(0)))))),\nT688 -> s(s(s(s(s(s(0))))))" }, { "from": 3321, "to": 3361, "label": "EVAL-BACKTRACK" }, { "from": 3324, "to": 3327, "label": "CASE" }, { "from": 3327, "to": 3328, "label": "PARALLEL" }, { "from": 3327, "to": 3329, "label": "PARALLEL" }, { "from": 3328, "to": 3331, "label": "EVAL with clause\nsmall(0).\nand substitutionT1457 -> 0" }, { "from": 3328, "to": 3332, "label": "EVAL-BACKTRACK" }, { "from": 3329, "to": 3356, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1457 -> s(0)" }, { "from": 3329, "to": 3357, "label": "EVAL-BACKTRACK" }, { "from": 3331, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(0))\nT775 -> T1458" }, { "from": 3356, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(s(0))\nT775 -> T1458" }, { "from": 3360, "to": 3362, "label": "CASE" }, { "from": 3362, "to": 3363, "label": "PARALLEL" }, { "from": 3362, "to": 3364, "label": "PARALLEL" }, { "from": 3363, "to": 3365, "label": "EVAL with clause\nsmall(0).\nand substitutionT1464 -> 0" }, { "from": 3363, "to": 3366, "label": "EVAL-BACKTRACK" }, { "from": 3364, "to": 3370, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1464 -> s(0)" }, { "from": 3364, "to": 3371, "label": "EVAL-BACKTRACK" }, { "from": 3365, "to": 3367, "label": "CASE" }, { "from": 3367, "to": 3368, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3368, "to": 3369, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3370, "to": 3372, "label": "CASE" }, { "from": 3372, "to": 3373, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3373, "to": 3374, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3377, "to": 3379, "label": "ONLY EVAL with clause\nlog2(X2698, s(s(X2699)), X2700, X2701) :- ','(small(X2698), log2(X2699, s(0), s(X2700), X2701)).\nand substitutionT675 -> T1473,\nX2698 -> T1473,\nX2699 -> s(0),\nX2700 -> s(s(s(s(s(s(0)))))),\nT676 -> T1474,\nX2701 -> T1474" }, { "from": 3378, "to": 3440, "label": "EVAL with clause\nlog2(X2720, X2721, X2722, X2722) :- ','(small(X2720), small(X2721)).\nand substitutionT675 -> T1477,\nX2720 -> T1477,\nX2721 -> s(s(s(0))),\nX2722 -> s(s(s(s(s(s(0)))))),\nT676 -> s(s(s(s(s(s(0))))))" }, { "from": 3378, "to": 3441, "label": "EVAL-BACKTRACK" }, { "from": 3379, "to": 3394, "label": "CASE" }, { "from": 3394, "to": 3395, "label": "PARALLEL" }, { "from": 3394, "to": 3396, "label": "PARALLEL" }, { "from": 3395, "to": 3397, "label": "EVAL with clause\nsmall(0).\nand substitutionT1473 -> 0" }, { "from": 3395, "to": 3398, "label": "EVAL-BACKTRACK" }, { "from": 3396, "to": 3426, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1473 -> s(0)" }, { "from": 3396, "to": 3427, "label": "EVAL-BACKTRACK" }, { "from": 3397, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(0)\nT775 -> T1474" }, { "from": 3426, "to": 1199, "label": "INSTANCE with matching:\nT774 -> s(0)\nT775 -> T1474" }, { "from": 3440, "to": 3442, "label": "CASE" }, { "from": 3442, "to": 3443, "label": "PARALLEL" }, { "from": 3442, "to": 3444, "label": "PARALLEL" }, { "from": 3443, "to": 3445, "label": "EVAL with clause\nsmall(0).\nand substitutionT1477 -> 0" }, { "from": 3443, "to": 3446, "label": "EVAL-BACKTRACK" }, { "from": 3444, "to": 3450, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1477 -> s(0)" }, { "from": 3444, "to": 3451, "label": "EVAL-BACKTRACK" }, { "from": 3445, "to": 3447, "label": "CASE" }, { "from": 3447, "to": 3448, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3448, "to": 3449, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3450, "to": 3452, "label": "CASE" }, { "from": 3452, "to": 3453, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3453, "to": 3454, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3470, "to": 3481, "label": "ONLY EVAL with clause\nlog2(X2747, s(s(X2748)), X2749, X2750) :- ','(small(X2747), log2(X2748, s(0), s(X2749), X2750)).\nand substitutionT663 -> T1486,\nX2747 -> T1486,\nX2748 -> 0,\nX2749 -> s(s(s(s(s(s(0)))))),\nT664 -> T1487,\nX2750 -> T1487" }, { "from": 3471, "to": 3496, "label": "EVAL with clause\nlog2(X2769, X2770, X2771, X2771) :- ','(small(X2769), small(X2770)).\nand substitutionT663 -> T1490,\nX2769 -> T1490,\nX2770 -> s(s(0)),\nX2771 -> s(s(s(s(s(s(0)))))),\nT664 -> s(s(s(s(s(s(0))))))" }, { "from": 3471, "to": 3497, "label": "EVAL-BACKTRACK" }, { "from": 3481, "to": 3482, "label": "CASE" }, { "from": 3482, "to": 3483, "label": "PARALLEL" }, { "from": 3482, "to": 3484, "label": "PARALLEL" }, { "from": 3483, "to": 3487, "label": "EVAL with clause\nsmall(0).\nand substitutionT1486 -> 0" }, { "from": 3483, "to": 3489, "label": "EVAL-BACKTRACK" }, { "from": 3484, "to": 3492, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1486 -> s(0)" }, { "from": 3484, "to": 3493, "label": "EVAL-BACKTRACK" }, { "from": 3487, "to": 1199, "label": "INSTANCE with matching:\nT774 -> 0\nT775 -> T1487" }, { "from": 3492, "to": 1199, "label": "INSTANCE with matching:\nT774 -> 0\nT775 -> T1487" }, { "from": 3496, "to": 3498, "label": "CASE" }, { "from": 3498, "to": 3499, "label": "PARALLEL" }, { "from": 3498, "to": 3500, "label": "PARALLEL" }, { "from": 3499, "to": 3501, "label": "EVAL with clause\nsmall(0).\nand substitutionT1490 -> 0" }, { "from": 3499, "to": 3502, "label": "EVAL-BACKTRACK" }, { "from": 3500, "to": 3506, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1490 -> s(0)" }, { "from": 3500, "to": 3507, "label": "EVAL-BACKTRACK" }, { "from": 3501, "to": 3503, "label": "CASE" }, { "from": 3503, "to": 3504, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3504, "to": 3505, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3506, "to": 3508, "label": "CASE" }, { "from": 3508, "to": 3509, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3509, "to": 3510, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3526, "to": 3528, "label": "EVAL with clause\nlog2(X2782, X2783, X2784, X2784) :- ','(small(X2782), small(X2783)).\nand substitutionT649 -> T1494,\nX2782 -> T1494,\nX2783 -> s(0),\nX2784 -> s(s(s(s(s(s(0)))))),\nT650 -> s(s(s(s(s(s(0))))))" }, { "from": 3526, "to": 3529, "label": "EVAL-BACKTRACK" }, { "from": 3528, "to": 3530, "label": "CASE" }, { "from": 3530, "to": 3531, "label": "PARALLEL" }, { "from": 3530, "to": 3532, "label": "PARALLEL" }, { "from": 3531, "to": 3533, "label": "EVAL with clause\nsmall(0).\nand substitutionT1494 -> 0" }, { "from": 3531, "to": 3534, "label": "EVAL-BACKTRACK" }, { "from": 3532, "to": 3539, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1494 -> s(0)" }, { "from": 3532, "to": 3540, "label": "EVAL-BACKTRACK" }, { "from": 3533, "to": 3535, "label": "CASE" }, { "from": 3535, "to": 3536, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3536, "to": 3537, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3537, "to": 3538, "label": "SUCCESS" }, { "from": 3539, "to": 3541, "label": "CASE" }, { "from": 3541, "to": 3542, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3542, "to": 3543, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 3543, "to": 3544, "label": "SUCCESS" }, { "from": 3545, "to": 1049, "label": "INSTANCE" }, { "from": 3551, "to": 3553, "label": "CASE" }, { "from": 3553, "to": 3554, "label": "PARALLEL" }, { "from": 3553, "to": 3555, "label": "PARALLEL" }, { "from": 3554, "to": 3556, "label": "EVAL with clause\nsmall(0).\nand substitutionT1501 -> 0" }, { "from": 3554, "to": 3557, "label": "EVAL-BACKTRACK" }, { "from": 3555, "to": 3563, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1501 -> s(0)" }, { "from": 3555, "to": 3564, "label": "EVAL-BACKTRACK" }, { "from": 3556, "to": 3558, "label": "CASE" }, { "from": 3558, "to": 3559, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3559, "to": 3560, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1502 -> 0" }, { "from": 3559, "to": 3561, "label": "EVAL-BACKTRACK" }, { "from": 3560, "to": 3562, "label": "SUCCESS" }, { "from": 3563, "to": 3565, "label": "CASE" }, { "from": 3565, "to": 3566, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3566, "to": 3567, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1502 -> 0" }, { "from": 3566, "to": 3568, "label": "EVAL-BACKTRACK" }, { "from": 3567, "to": 3569, "label": "SUCCESS" }, { "from": 3585, "to": 3590, "label": "ONLY EVAL with clause\nlog2(X2822, s(s(X2823)), X2824, X2825) :- ','(small(X2822), log2(X2823, s(0), s(X2824), X2825)).\nand substitutionT598 -> T1513,\nX2822 -> T1513,\nX2823 -> s(s(s(s(s(0))))),\nX2824 -> s(s(s(s(s(0))))),\nT599 -> T1514,\nX2825 -> T1514" }, { "from": 3586, "to": 3612, "label": "EVAL with clause\nlog2(X2844, X2845, X2846, X2846) :- ','(small(X2844), small(X2845)).\nand substitutionT598 -> T1520,\nX2844 -> T1520,\nX2845 -> s(s(s(s(s(s(s(0))))))),\nX2846 -> s(s(s(s(s(0))))),\nT599 -> s(s(s(s(s(0)))))" }, { "from": 3586, "to": 3613, "label": "EVAL-BACKTRACK" }, { "from": 3590, "to": 3596, "label": "CASE" }, { "from": 3596, "to": 3597, "label": "PARALLEL" }, { "from": 3596, "to": 3598, "label": "PARALLEL" }, { "from": 3597, "to": 3599, "label": "EVAL with clause\nsmall(0).\nand substitutionT1513 -> 0" }, { "from": 3597, "to": 3600, "label": "EVAL-BACKTRACK" }, { "from": 3598, "to": 3602, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1513 -> s(0)" }, { "from": 3598, "to": 3604, "label": "EVAL-BACKTRACK" }, { "from": 3599, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(s(s(0)))))\nT650 -> T1514" }, { "from": 3602, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(s(s(0)))))\nT650 -> T1514" }, { "from": 3612, "to": 3614, "label": "CASE" }, { "from": 3614, "to": 3615, "label": "PARALLEL" }, { "from": 3614, "to": 3616, "label": "PARALLEL" }, { "from": 3615, "to": 3617, "label": "EVAL with clause\nsmall(0).\nand substitutionT1520 -> 0" }, { "from": 3615, "to": 3618, "label": "EVAL-BACKTRACK" }, { "from": 3616, "to": 3622, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1520 -> s(0)" }, { "from": 3616, "to": 3623, "label": "EVAL-BACKTRACK" }, { "from": 3617, "to": 3619, "label": "CASE" }, { "from": 3619, "to": 3620, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3620, "to": 3621, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3622, "to": 3624, "label": "CASE" }, { "from": 3624, "to": 3625, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3625, "to": 3626, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3659, "to": 3663, "label": "ONLY EVAL with clause\nlog2(X2871, s(s(X2872)), X2873, X2874) :- ','(small(X2871), log2(X2872, s(0), s(X2873), X2874)).\nand substitutionT586 -> T1531,\nX2871 -> T1531,\nX2872 -> s(s(s(s(0)))),\nX2873 -> s(s(s(s(s(0))))),\nT587 -> T1532,\nX2874 -> T1532" }, { "from": 3660, "to": 3704, "label": "EVAL with clause\nlog2(X2893, X2894, X2895, X2895) :- ','(small(X2893), small(X2894)).\nand substitutionT586 -> T1538,\nX2893 -> T1538,\nX2894 -> s(s(s(s(s(s(0)))))),\nX2895 -> s(s(s(s(s(0))))),\nT587 -> s(s(s(s(s(0)))))" }, { "from": 3660, "to": 3705, "label": "EVAL-BACKTRACK" }, { "from": 3663, "to": 3664, "label": "CASE" }, { "from": 3664, "to": 3665, "label": "PARALLEL" }, { "from": 3664, "to": 3666, "label": "PARALLEL" }, { "from": 3665, "to": 3667, "label": "EVAL with clause\nsmall(0).\nand substitutionT1531 -> 0" }, { "from": 3665, "to": 3668, "label": "EVAL-BACKTRACK" }, { "from": 3666, "to": 3669, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1531 -> s(0)" }, { "from": 3666, "to": 3670, "label": "EVAL-BACKTRACK" }, { "from": 3667, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(s(0))))\nT650 -> T1532" }, { "from": 3669, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(s(0))))\nT650 -> T1532" }, { "from": 3704, "to": 3706, "label": "CASE" }, { "from": 3706, "to": 3707, "label": "PARALLEL" }, { "from": 3706, "to": 3708, "label": "PARALLEL" }, { "from": 3707, "to": 3709, "label": "EVAL with clause\nsmall(0).\nand substitutionT1538 -> 0" }, { "from": 3707, "to": 3710, "label": "EVAL-BACKTRACK" }, { "from": 3708, "to": 3714, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1538 -> s(0)" }, { "from": 3708, "to": 3715, "label": "EVAL-BACKTRACK" }, { "from": 3709, "to": 3711, "label": "CASE" }, { "from": 3711, "to": 3712, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3712, "to": 3713, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3714, "to": 3716, "label": "CASE" }, { "from": 3716, "to": 3717, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3717, "to": 3718, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3734, "to": 3748, "label": "ONLY EVAL with clause\nlog2(X2920, s(s(X2921)), X2922, X2923) :- ','(small(X2920), log2(X2921, s(0), s(X2922), X2923)).\nand substitutionT574 -> T1549,\nX2920 -> T1549,\nX2921 -> s(s(s(0))),\nX2922 -> s(s(s(s(s(0))))),\nT575 -> T1550,\nX2923 -> T1550" }, { "from": 3735, "to": 3787, "label": "EVAL with clause\nlog2(X2942, X2943, X2944, X2944) :- ','(small(X2942), small(X2943)).\nand substitutionT574 -> T1556,\nX2942 -> T1556,\nX2943 -> s(s(s(s(s(0))))),\nX2944 -> s(s(s(s(s(0))))),\nT575 -> s(s(s(s(s(0)))))" }, { "from": 3735, "to": 3788, "label": "EVAL-BACKTRACK" }, { "from": 3748, "to": 3749, "label": "CASE" }, { "from": 3749, "to": 3750, "label": "PARALLEL" }, { "from": 3749, "to": 3751, "label": "PARALLEL" }, { "from": 3750, "to": 3752, "label": "EVAL with clause\nsmall(0).\nand substitutionT1549 -> 0" }, { "from": 3750, "to": 3753, "label": "EVAL-BACKTRACK" }, { "from": 3751, "to": 3769, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1549 -> s(0)" }, { "from": 3751, "to": 3770, "label": "EVAL-BACKTRACK" }, { "from": 3752, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(0)))\nT650 -> T1550" }, { "from": 3769, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(s(0)))\nT650 -> T1550" }, { "from": 3787, "to": 3789, "label": "CASE" }, { "from": 3789, "to": 3790, "label": "PARALLEL" }, { "from": 3789, "to": 3791, "label": "PARALLEL" }, { "from": 3790, "to": 3792, "label": "EVAL with clause\nsmall(0).\nand substitutionT1556 -> 0" }, { "from": 3790, "to": 3793, "label": "EVAL-BACKTRACK" }, { "from": 3791, "to": 3797, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1556 -> s(0)" }, { "from": 3791, "to": 3798, "label": "EVAL-BACKTRACK" }, { "from": 3792, "to": 3794, "label": "CASE" }, { "from": 3794, "to": 3795, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3795, "to": 3796, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3797, "to": 3799, "label": "CASE" }, { "from": 3799, "to": 3800, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3800, "to": 3801, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3811, "to": 3827, "label": "ONLY EVAL with clause\nlog2(X2969, s(s(X2970)), X2971, X2972) :- ','(small(X2969), log2(X2970, s(0), s(X2971), X2972)).\nand substitutionT562 -> T1567,\nX2969 -> T1567,\nX2970 -> s(s(0)),\nX2971 -> s(s(s(s(s(0))))),\nT563 -> T1568,\nX2972 -> T1568" }, { "from": 3813, "to": 3865, "label": "EVAL with clause\nlog2(X2991, X2992, X2993, X2993) :- ','(small(X2991), small(X2992)).\nand substitutionT562 -> T1574,\nX2991 -> T1574,\nX2992 -> s(s(s(s(0)))),\nX2993 -> s(s(s(s(s(0))))),\nT563 -> s(s(s(s(s(0)))))" }, { "from": 3813, "to": 3866, "label": "EVAL-BACKTRACK" }, { "from": 3827, "to": 3828, "label": "CASE" }, { "from": 3828, "to": 3829, "label": "PARALLEL" }, { "from": 3828, "to": 3830, "label": "PARALLEL" }, { "from": 3829, "to": 3831, "label": "EVAL with clause\nsmall(0).\nand substitutionT1567 -> 0" }, { "from": 3829, "to": 3832, "label": "EVAL-BACKTRACK" }, { "from": 3830, "to": 3833, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1567 -> s(0)" }, { "from": 3830, "to": 3834, "label": "EVAL-BACKTRACK" }, { "from": 3831, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(0))\nT650 -> T1568" }, { "from": 3833, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(s(0))\nT650 -> T1568" }, { "from": 3865, "to": 3867, "label": "CASE" }, { "from": 3867, "to": 3868, "label": "PARALLEL" }, { "from": 3867, "to": 3869, "label": "PARALLEL" }, { "from": 3868, "to": 3870, "label": "EVAL with clause\nsmall(0).\nand substitutionT1574 -> 0" }, { "from": 3868, "to": 3871, "label": "EVAL-BACKTRACK" }, { "from": 3869, "to": 3875, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1574 -> s(0)" }, { "from": 3869, "to": 3876, "label": "EVAL-BACKTRACK" }, { "from": 3870, "to": 3872, "label": "CASE" }, { "from": 3872, "to": 3873, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3873, "to": 3874, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3875, "to": 3877, "label": "CASE" }, { "from": 3877, "to": 3878, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3878, "to": 3879, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3880, "to": 3920, "label": "ONLY EVAL with clause\nlog2(X3018, s(s(X3019)), X3020, X3021) :- ','(small(X3018), log2(X3019, s(0), s(X3020), X3021)).\nand substitutionT550 -> T1583,\nX3018 -> T1583,\nX3019 -> s(0),\nX3020 -> s(s(s(s(s(0))))),\nT551 -> T1584,\nX3021 -> T1584" }, { "from": 3881, "to": 3936, "label": "EVAL with clause\nlog2(X3040, X3041, X3042, X3042) :- ','(small(X3040), small(X3041)).\nand substitutionT550 -> T1587,\nX3040 -> T1587,\nX3041 -> s(s(s(0))),\nX3042 -> s(s(s(s(s(0))))),\nT551 -> s(s(s(s(s(0)))))" }, { "from": 3881, "to": 3937, "label": "EVAL-BACKTRACK" }, { "from": 3920, "to": 3923, "label": "CASE" }, { "from": 3923, "to": 3924, "label": "PARALLEL" }, { "from": 3923, "to": 3925, "label": "PARALLEL" }, { "from": 3924, "to": 3926, "label": "EVAL with clause\nsmall(0).\nand substitutionT1583 -> 0" }, { "from": 3924, "to": 3927, "label": "EVAL-BACKTRACK" }, { "from": 3925, "to": 3928, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1583 -> s(0)" }, { "from": 3925, "to": 3929, "label": "EVAL-BACKTRACK" }, { "from": 3926, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(0)\nT650 -> T1584" }, { "from": 3928, "to": 1049, "label": "INSTANCE with matching:\nT649 -> s(0)\nT650 -> T1584" }, { "from": 3936, "to": 3938, "label": "CASE" }, { "from": 3938, "to": 3939, "label": "PARALLEL" }, { "from": 3938, "to": 3940, "label": "PARALLEL" }, { "from": 3939, "to": 3941, "label": "EVAL with clause\nsmall(0).\nand substitutionT1587 -> 0" }, { "from": 3939, "to": 3942, "label": "EVAL-BACKTRACK" }, { "from": 3940, "to": 3946, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1587 -> s(0)" }, { "from": 3940, "to": 3947, "label": "EVAL-BACKTRACK" }, { "from": 3941, "to": 3943, "label": "CASE" }, { "from": 3943, "to": 3944, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3944, "to": 3945, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3946, "to": 3948, "label": "CASE" }, { "from": 3948, "to": 3949, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 3949, "to": 3950, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 3963, "to": 3991, "label": "ONLY EVAL with clause\nlog2(X3067, s(s(X3068)), X3069, X3070) :- ','(small(X3067), log2(X3068, s(0), s(X3069), X3070)).\nand substitutionT538 -> T1596,\nX3067 -> T1596,\nX3068 -> 0,\nX3069 -> s(s(s(s(s(0))))),\nT539 -> T1597,\nX3070 -> T1597" }, { "from": 3965, "to": 4007, "label": "EVAL with clause\nlog2(X3089, X3090, X3091, X3091) :- ','(small(X3089), small(X3090)).\nand substitutionT538 -> T1600,\nX3089 -> T1600,\nX3090 -> s(s(0)),\nX3091 -> s(s(s(s(s(0))))),\nT539 -> s(s(s(s(s(0)))))" }, { "from": 3965, "to": 4008, "label": "EVAL-BACKTRACK" }, { "from": 3991, "to": 3992, "label": "CASE" }, { "from": 3992, "to": 3993, "label": "PARALLEL" }, { "from": 3992, "to": 3994, "label": "PARALLEL" }, { "from": 3993, "to": 3995, "label": "EVAL with clause\nsmall(0).\nand substitutionT1596 -> 0" }, { "from": 3993, "to": 3996, "label": "EVAL-BACKTRACK" }, { "from": 3994, "to": 3999, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1596 -> s(0)" }, { "from": 3994, "to": 4000, "label": "EVAL-BACKTRACK" }, { "from": 3995, "to": 1049, "label": "INSTANCE with matching:\nT649 -> 0\nT650 -> T1597" }, { "from": 3999, "to": 1049, "label": "INSTANCE with matching:\nT649 -> 0\nT650 -> T1597" }, { "from": 4007, "to": 4009, "label": "CASE" }, { "from": 4009, "to": 4010, "label": "PARALLEL" }, { "from": 4009, "to": 4011, "label": "PARALLEL" }, { "from": 4010, "to": 4012, "label": "EVAL with clause\nsmall(0).\nand substitutionT1600 -> 0" }, { "from": 4010, "to": 4013, "label": "EVAL-BACKTRACK" }, { "from": 4011, "to": 4018, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1600 -> s(0)" }, { "from": 4011, "to": 4019, "label": "EVAL-BACKTRACK" }, { "from": 4012, "to": 4014, "label": "CASE" }, { "from": 4014, "to": 4016, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4016, "to": 4017, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4018, "to": 4020, "label": "CASE" }, { "from": 4020, "to": 4021, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4021, "to": 4022, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4026, "to": 4033, "label": "EVAL with clause\nlog2(X3102, X3103, X3104, X3104) :- ','(small(X3102), small(X3103)).\nand substitutionT524 -> T1604,\nX3102 -> T1604,\nX3103 -> s(0),\nX3104 -> s(s(s(s(s(0))))),\nT525 -> s(s(s(s(s(0)))))" }, { "from": 4026, "to": 4034, "label": "EVAL-BACKTRACK" }, { "from": 4033, "to": 4035, "label": "CASE" }, { "from": 4035, "to": 4036, "label": "PARALLEL" }, { "from": 4035, "to": 4037, "label": "PARALLEL" }, { "from": 4036, "to": 4038, "label": "EVAL with clause\nsmall(0).\nand substitutionT1604 -> 0" }, { "from": 4036, "to": 4039, "label": "EVAL-BACKTRACK" }, { "from": 4037, "to": 4044, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1604 -> s(0)" }, { "from": 4037, "to": 4045, "label": "EVAL-BACKTRACK" }, { "from": 4038, "to": 4040, "label": "CASE" }, { "from": 4040, "to": 4041, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4041, "to": 4042, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4042, "to": 4043, "label": "SUCCESS" }, { "from": 4044, "to": 4046, "label": "CASE" }, { "from": 4046, "to": 4047, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4047, "to": 4048, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4048, "to": 4049, "label": "SUCCESS" }, { "from": 4050, "to": 843, "label": "INSTANCE" }, { "from": 4084, "to": 4086, "label": "CASE" }, { "from": 4086, "to": 4087, "label": "PARALLEL" }, { "from": 4086, "to": 4088, "label": "PARALLEL" }, { "from": 4087, "to": 4089, "label": "EVAL with clause\nsmall(0).\nand substitutionT1611 -> 0" }, { "from": 4087, "to": 4090, "label": "EVAL-BACKTRACK" }, { "from": 4088, "to": 4096, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1611 -> s(0)" }, { "from": 4088, "to": 4097, "label": "EVAL-BACKTRACK" }, { "from": 4089, "to": 4091, "label": "CASE" }, { "from": 4091, "to": 4092, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4092, "to": 4093, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1612 -> 0" }, { "from": 4092, "to": 4094, "label": "EVAL-BACKTRACK" }, { "from": 4093, "to": 4095, "label": "SUCCESS" }, { "from": 4096, "to": 4098, "label": "CASE" }, { "from": 4098, "to": 4099, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4099, "to": 4100, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1612 -> 0" }, { "from": 4099, "to": 4101, "label": "EVAL-BACKTRACK" }, { "from": 4100, "to": 4102, "label": "SUCCESS" }, { "from": 4105, "to": 4119, "label": "ONLY EVAL with clause\nlog2(X3142, s(s(X3143)), X3144, X3145) :- ','(small(X3142), log2(X3143, s(0), s(X3144), X3145)).\nand substitutionT473 -> T1623,\nX3142 -> T1623,\nX3143 -> s(s(s(s(s(0))))),\nX3144 -> s(s(s(s(0)))),\nT474 -> T1624,\nX3145 -> T1624" }, { "from": 4106, "to": 4161, "label": "EVAL with clause\nlog2(X3164, X3165, X3166, X3166) :- ','(small(X3164), small(X3165)).\nand substitutionT473 -> T1630,\nX3164 -> T1630,\nX3165 -> s(s(s(s(s(s(s(0))))))),\nX3166 -> s(s(s(s(0)))),\nT474 -> s(s(s(s(0))))" }, { "from": 4106, "to": 4162, "label": "EVAL-BACKTRACK" }, { "from": 4119, "to": 4122, "label": "CASE" }, { "from": 4122, "to": 4123, "label": "PARALLEL" }, { "from": 4122, "to": 4124, "label": "PARALLEL" }, { "from": 4123, "to": 4125, "label": "EVAL with clause\nsmall(0).\nand substitutionT1623 -> 0" }, { "from": 4123, "to": 4126, "label": "EVAL-BACKTRACK" }, { "from": 4124, "to": 4129, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1623 -> s(0)" }, { "from": 4124, "to": 4130, "label": "EVAL-BACKTRACK" }, { "from": 4125, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(s(s(0)))))\nT525 -> T1624" }, { "from": 4129, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(s(s(0)))))\nT525 -> T1624" }, { "from": 4161, "to": 4163, "label": "CASE" }, { "from": 4163, "to": 4164, "label": "PARALLEL" }, { "from": 4163, "to": 4165, "label": "PARALLEL" }, { "from": 4164, "to": 4166, "label": "EVAL with clause\nsmall(0).\nand substitutionT1630 -> 0" }, { "from": 4164, "to": 4167, "label": "EVAL-BACKTRACK" }, { "from": 4165, "to": 4171, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1630 -> s(0)" }, { "from": 4165, "to": 4172, "label": "EVAL-BACKTRACK" }, { "from": 4166, "to": 4168, "label": "CASE" }, { "from": 4168, "to": 4169, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4169, "to": 4170, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4171, "to": 4173, "label": "CASE" }, { "from": 4173, "to": 4174, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4174, "to": 4175, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4180, "to": 4182, "label": "ONLY EVAL with clause\nlog2(X3191, s(s(X3192)), X3193, X3194) :- ','(small(X3191), log2(X3192, s(0), s(X3193), X3194)).\nand substitutionT461 -> T1641,\nX3191 -> T1641,\nX3192 -> s(s(s(s(0)))),\nX3193 -> s(s(s(s(0)))),\nT462 -> T1642,\nX3194 -> T1642" }, { "from": 4181, "to": 4206, "label": "EVAL with clause\nlog2(X3213, X3214, X3215, X3215) :- ','(small(X3213), small(X3214)).\nand substitutionT461 -> T1648,\nX3213 -> T1648,\nX3214 -> s(s(s(s(s(s(0)))))),\nX3215 -> s(s(s(s(0)))),\nT462 -> s(s(s(s(0))))" }, { "from": 4181, "to": 4207, "label": "EVAL-BACKTRACK" }, { "from": 4182, "to": 4185, "label": "CASE" }, { "from": 4185, "to": 4186, "label": "PARALLEL" }, { "from": 4185, "to": 4187, "label": "PARALLEL" }, { "from": 4186, "to": 4188, "label": "EVAL with clause\nsmall(0).\nand substitutionT1641 -> 0" }, { "from": 4186, "to": 4190, "label": "EVAL-BACKTRACK" }, { "from": 4187, "to": 4200, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1641 -> s(0)" }, { "from": 4187, "to": 4201, "label": "EVAL-BACKTRACK" }, { "from": 4188, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(s(0))))\nT525 -> T1642" }, { "from": 4200, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(s(0))))\nT525 -> T1642" }, { "from": 4206, "to": 4208, "label": "CASE" }, { "from": 4208, "to": 4209, "label": "PARALLEL" }, { "from": 4208, "to": 4210, "label": "PARALLEL" }, { "from": 4209, "to": 4211, "label": "EVAL with clause\nsmall(0).\nand substitutionT1648 -> 0" }, { "from": 4209, "to": 4212, "label": "EVAL-BACKTRACK" }, { "from": 4210, "to": 4218, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1648 -> s(0)" }, { "from": 4210, "to": 4219, "label": "EVAL-BACKTRACK" }, { "from": 4211, "to": 4213, "label": "CASE" }, { "from": 4213, "to": 4214, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4214, "to": 4215, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4218, "to": 4221, "label": "CASE" }, { "from": 4221, "to": 4222, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4222, "to": 4225, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4253, "to": 4258, "label": "ONLY EVAL with clause\nlog2(X3240, s(s(X3241)), X3242, X3243) :- ','(small(X3240), log2(X3241, s(0), s(X3242), X3243)).\nand substitutionT449 -> T1659,\nX3240 -> T1659,\nX3241 -> s(s(s(0))),\nX3242 -> s(s(s(s(0)))),\nT450 -> T1660,\nX3243 -> T1660" }, { "from": 4254, "to": 4296, "label": "EVAL with clause\nlog2(X3262, X3263, X3264, X3264) :- ','(small(X3262), small(X3263)).\nand substitutionT449 -> T1666,\nX3262 -> T1666,\nX3263 -> s(s(s(s(s(0))))),\nX3264 -> s(s(s(s(0)))),\nT450 -> s(s(s(s(0))))" }, { "from": 4254, "to": 4297, "label": "EVAL-BACKTRACK" }, { "from": 4258, "to": 4265, "label": "CASE" }, { "from": 4265, "to": 4266, "label": "PARALLEL" }, { "from": 4265, "to": 4267, "label": "PARALLEL" }, { "from": 4266, "to": 4268, "label": "EVAL with clause\nsmall(0).\nand substitutionT1659 -> 0" }, { "from": 4266, "to": 4269, "label": "EVAL-BACKTRACK" }, { "from": 4267, "to": 4277, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1659 -> s(0)" }, { "from": 4267, "to": 4278, "label": "EVAL-BACKTRACK" }, { "from": 4268, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(0)))\nT525 -> T1660" }, { "from": 4277, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(s(0)))\nT525 -> T1660" }, { "from": 4296, "to": 4298, "label": "CASE" }, { "from": 4298, "to": 4299, "label": "PARALLEL" }, { "from": 4298, "to": 4300, "label": "PARALLEL" }, { "from": 4299, "to": 4301, "label": "EVAL with clause\nsmall(0).\nand substitutionT1666 -> 0" }, { "from": 4299, "to": 4302, "label": "EVAL-BACKTRACK" }, { "from": 4300, "to": 4306, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1666 -> s(0)" }, { "from": 4300, "to": 4307, "label": "EVAL-BACKTRACK" }, { "from": 4301, "to": 4303, "label": "CASE" }, { "from": 4303, "to": 4304, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4304, "to": 4305, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4306, "to": 4308, "label": "CASE" }, { "from": 4308, "to": 4309, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4309, "to": 4310, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4328, "to": 4333, "label": "ONLY EVAL with clause\nlog2(X3289, s(s(X3290)), X3291, X3292) :- ','(small(X3289), log2(X3290, s(0), s(X3291), X3292)).\nand substitutionT437 -> T1677,\nX3289 -> T1677,\nX3290 -> s(s(0)),\nX3291 -> s(s(s(s(0)))),\nT438 -> T1678,\nX3292 -> T1678" }, { "from": 4329, "to": 4356, "label": "EVAL with clause\nlog2(X3311, X3312, X3313, X3313) :- ','(small(X3311), small(X3312)).\nand substitutionT437 -> T1684,\nX3311 -> T1684,\nX3312 -> s(s(s(s(0)))),\nX3313 -> s(s(s(s(0)))),\nT438 -> s(s(s(s(0))))" }, { "from": 4329, "to": 4357, "label": "EVAL-BACKTRACK" }, { "from": 4333, "to": 4339, "label": "CASE" }, { "from": 4339, "to": 4340, "label": "PARALLEL" }, { "from": 4339, "to": 4341, "label": "PARALLEL" }, { "from": 4340, "to": 4342, "label": "EVAL with clause\nsmall(0).\nand substitutionT1677 -> 0" }, { "from": 4340, "to": 4343, "label": "EVAL-BACKTRACK" }, { "from": 4341, "to": 4350, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1677 -> s(0)" }, { "from": 4341, "to": 4352, "label": "EVAL-BACKTRACK" }, { "from": 4342, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(0))\nT525 -> T1678" }, { "from": 4350, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(s(0))\nT525 -> T1678" }, { "from": 4356, "to": 4358, "label": "CASE" }, { "from": 4358, "to": 4359, "label": "PARALLEL" }, { "from": 4358, "to": 4360, "label": "PARALLEL" }, { "from": 4359, "to": 4361, "label": "EVAL with clause\nsmall(0).\nand substitutionT1684 -> 0" }, { "from": 4359, "to": 4363, "label": "EVAL-BACKTRACK" }, { "from": 4360, "to": 4371, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1684 -> s(0)" }, { "from": 4360, "to": 4373, "label": "EVAL-BACKTRACK" }, { "from": 4361, "to": 4365, "label": "CASE" }, { "from": 4365, "to": 4366, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4366, "to": 4368, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4371, "to": 4375, "label": "CASE" }, { "from": 4375, "to": 4377, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4377, "to": 4379, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4402, "to": 4425, "label": "ONLY EVAL with clause\nlog2(X3338, s(s(X3339)), X3340, X3341) :- ','(small(X3338), log2(X3339, s(0), s(X3340), X3341)).\nand substitutionT425 -> T1693,\nX3338 -> T1693,\nX3339 -> s(0),\nX3340 -> s(s(s(s(0)))),\nT426 -> T1694,\nX3341 -> T1694" }, { "from": 4403, "to": 4462, "label": "EVAL with clause\nlog2(X3360, X3361, X3362, X3362) :- ','(small(X3360), small(X3361)).\nand substitutionT425 -> T1697,\nX3360 -> T1697,\nX3361 -> s(s(s(0))),\nX3362 -> s(s(s(s(0)))),\nT426 -> s(s(s(s(0))))" }, { "from": 4403, "to": 4463, "label": "EVAL-BACKTRACK" }, { "from": 4425, "to": 4426, "label": "CASE" }, { "from": 4426, "to": 4429, "label": "PARALLEL" }, { "from": 4426, "to": 4430, "label": "PARALLEL" }, { "from": 4429, "to": 4432, "label": "EVAL with clause\nsmall(0).\nand substitutionT1693 -> 0" }, { "from": 4429, "to": 4433, "label": "EVAL-BACKTRACK" }, { "from": 4430, "to": 4450, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1693 -> s(0)" }, { "from": 4430, "to": 4451, "label": "EVAL-BACKTRACK" }, { "from": 4432, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(0)\nT525 -> T1694" }, { "from": 4450, "to": 843, "label": "INSTANCE with matching:\nT524 -> s(0)\nT525 -> T1694" }, { "from": 4462, "to": 4464, "label": "CASE" }, { "from": 4464, "to": 4465, "label": "PARALLEL" }, { "from": 4464, "to": 4466, "label": "PARALLEL" }, { "from": 4465, "to": 4467, "label": "EVAL with clause\nsmall(0).\nand substitutionT1697 -> 0" }, { "from": 4465, "to": 4468, "label": "EVAL-BACKTRACK" }, { "from": 4466, "to": 4472, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1697 -> s(0)" }, { "from": 4466, "to": 4473, "label": "EVAL-BACKTRACK" }, { "from": 4467, "to": 4469, "label": "CASE" }, { "from": 4469, "to": 4470, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4470, "to": 4471, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4472, "to": 4474, "label": "CASE" }, { "from": 4474, "to": 4475, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4475, "to": 4476, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4477, "to": 4503, "label": "ONLY EVAL with clause\nlog2(X3387, s(s(X3388)), X3389, X3390) :- ','(small(X3387), log2(X3388, s(0), s(X3389), X3390)).\nand substitutionT413 -> T1706,\nX3387 -> T1706,\nX3388 -> 0,\nX3389 -> s(s(s(s(0)))),\nT414 -> T1707,\nX3390 -> T1707" }, { "from": 4478, "to": 4564, "label": "EVAL with clause\nlog2(X3409, X3410, X3411, X3411) :- ','(small(X3409), small(X3410)).\nand substitutionT413 -> T1710,\nX3409 -> T1710,\nX3410 -> s(s(0)),\nX3411 -> s(s(s(s(0)))),\nT414 -> s(s(s(s(0))))" }, { "from": 4478, "to": 4565, "label": "EVAL-BACKTRACK" }, { "from": 4503, "to": 4523, "label": "CASE" }, { "from": 4523, "to": 4524, "label": "PARALLEL" }, { "from": 4523, "to": 4525, "label": "PARALLEL" }, { "from": 4524, "to": 4526, "label": "EVAL with clause\nsmall(0).\nand substitutionT1706 -> 0" }, { "from": 4524, "to": 4527, "label": "EVAL-BACKTRACK" }, { "from": 4525, "to": 4543, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1706 -> s(0)" }, { "from": 4525, "to": 4544, "label": "EVAL-BACKTRACK" }, { "from": 4526, "to": 843, "label": "INSTANCE with matching:\nT524 -> 0\nT525 -> T1707" }, { "from": 4543, "to": 843, "label": "INSTANCE with matching:\nT524 -> 0\nT525 -> T1707" }, { "from": 4564, "to": 4566, "label": "CASE" }, { "from": 4566, "to": 4567, "label": "PARALLEL" }, { "from": 4566, "to": 4568, "label": "PARALLEL" }, { "from": 4567, "to": 4569, "label": "EVAL with clause\nsmall(0).\nand substitutionT1710 -> 0" }, { "from": 4567, "to": 4570, "label": "EVAL-BACKTRACK" }, { "from": 4568, "to": 4574, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1710 -> s(0)" }, { "from": 4568, "to": 4575, "label": "EVAL-BACKTRACK" }, { "from": 4569, "to": 4571, "label": "CASE" }, { "from": 4571, "to": 4572, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4572, "to": 4573, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4574, "to": 4576, "label": "CASE" }, { "from": 4576, "to": 4577, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4577, "to": 4578, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4581, "to": 4584, "label": "EVAL with clause\nlog2(X3422, X3423, X3424, X3424) :- ','(small(X3422), small(X3423)).\nand substitutionT399 -> T1714,\nX3422 -> T1714,\nX3423 -> s(0),\nX3424 -> s(s(s(s(0)))),\nT400 -> s(s(s(s(0))))" }, { "from": 4581, "to": 4585, "label": "EVAL-BACKTRACK" }, { "from": 4584, "to": 4586, "label": "CASE" }, { "from": 4586, "to": 4587, "label": "PARALLEL" }, { "from": 4586, "to": 4588, "label": "PARALLEL" }, { "from": 4587, "to": 4589, "label": "EVAL with clause\nsmall(0).\nand substitutionT1714 -> 0" }, { "from": 4587, "to": 4590, "label": "EVAL-BACKTRACK" }, { "from": 4588, "to": 4595, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1714 -> s(0)" }, { "from": 4588, "to": 4596, "label": "EVAL-BACKTRACK" }, { "from": 4589, "to": 4591, "label": "CASE" }, { "from": 4591, "to": 4592, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4592, "to": 4593, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4593, "to": 4594, "label": "SUCCESS" }, { "from": 4595, "to": 4597, "label": "CASE" }, { "from": 4597, "to": 4598, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4598, "to": 4599, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 4599, "to": 4600, "label": "SUCCESS" }, { "from": 4601, "to": 660, "label": "INSTANCE" }, { "from": 4612, "to": 4614, "label": "CASE" }, { "from": 4614, "to": 4615, "label": "PARALLEL" }, { "from": 4614, "to": 4616, "label": "PARALLEL" }, { "from": 4615, "to": 4617, "label": "EVAL with clause\nsmall(0).\nand substitutionT1721 -> 0" }, { "from": 4615, "to": 4618, "label": "EVAL-BACKTRACK" }, { "from": 4616, "to": 4624, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1721 -> s(0)" }, { "from": 4616, "to": 4625, "label": "EVAL-BACKTRACK" }, { "from": 4617, "to": 4619, "label": "CASE" }, { "from": 4619, "to": 4620, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4620, "to": 4621, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1722 -> 0" }, { "from": 4620, "to": 4622, "label": "EVAL-BACKTRACK" }, { "from": 4621, "to": 4623, "label": "SUCCESS" }, { "from": 4624, "to": 4626, "label": "CASE" }, { "from": 4626, "to": 4627, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4627, "to": 4628, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1722 -> 0" }, { "from": 4627, "to": 4629, "label": "EVAL-BACKTRACK" }, { "from": 4628, "to": 4630, "label": "SUCCESS" }, { "from": 4648, "to": 4672, "label": "ONLY EVAL with clause\nlog2(X3462, s(s(X3463)), X3464, X3465) :- ','(small(X3462), log2(X3463, s(0), s(X3464), X3465)).\nand substitutionT348 -> T1733,\nX3462 -> T1733,\nX3463 -> s(s(s(s(s(0))))),\nX3464 -> s(s(s(0))),\nT349 -> T1734,\nX3465 -> T1734" }, { "from": 4649, "to": 4688, "label": "EVAL with clause\nlog2(X3484, X3485, X3486, X3486) :- ','(small(X3484), small(X3485)).\nand substitutionT348 -> T1740,\nX3484 -> T1740,\nX3485 -> s(s(s(s(s(s(s(0))))))),\nX3486 -> s(s(s(0))),\nT349 -> s(s(s(0)))" }, { "from": 4649, "to": 4689, "label": "EVAL-BACKTRACK" }, { "from": 4672, "to": 4673, "label": "CASE" }, { "from": 4673, "to": 4674, "label": "PARALLEL" }, { "from": 4673, "to": 4675, "label": "PARALLEL" }, { "from": 4674, "to": 4676, "label": "EVAL with clause\nsmall(0).\nand substitutionT1733 -> 0" }, { "from": 4674, "to": 4677, "label": "EVAL-BACKTRACK" }, { "from": 4675, "to": 4680, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1733 -> s(0)" }, { "from": 4675, "to": 4681, "label": "EVAL-BACKTRACK" }, { "from": 4676, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(s(s(0)))))\nT400 -> T1734" }, { "from": 4680, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(s(s(0)))))\nT400 -> T1734" }, { "from": 4688, "to": 4690, "label": "CASE" }, { "from": 4690, "to": 4691, "label": "PARALLEL" }, { "from": 4690, "to": 4692, "label": "PARALLEL" }, { "from": 4691, "to": 4693, "label": "EVAL with clause\nsmall(0).\nand substitutionT1740 -> 0" }, { "from": 4691, "to": 4694, "label": "EVAL-BACKTRACK" }, { "from": 4692, "to": 4698, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1740 -> s(0)" }, { "from": 4692, "to": 4699, "label": "EVAL-BACKTRACK" }, { "from": 4693, "to": 4695, "label": "CASE" }, { "from": 4695, "to": 4696, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4696, "to": 4697, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4698, "to": 4700, "label": "CASE" }, { "from": 4700, "to": 4702, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4702, "to": 4703, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4713, "to": 4747, "label": "ONLY EVAL with clause\nlog2(X3511, s(s(X3512)), X3513, X3514) :- ','(small(X3511), log2(X3512, s(0), s(X3513), X3514)).\nand substitutionT336 -> T1751,\nX3511 -> T1751,\nX3512 -> s(s(s(s(0)))),\nX3513 -> s(s(s(0))),\nT337 -> T1752,\nX3514 -> T1752" }, { "from": 4714, "to": 4758, "label": "EVAL with clause\nlog2(X3533, X3534, X3535, X3535) :- ','(small(X3533), small(X3534)).\nand substitutionT336 -> T1758,\nX3533 -> T1758,\nX3534 -> s(s(s(s(s(s(0)))))),\nX3535 -> s(s(s(0))),\nT337 -> s(s(s(0)))" }, { "from": 4714, "to": 4759, "label": "EVAL-BACKTRACK" }, { "from": 4747, "to": 4748, "label": "CASE" }, { "from": 4748, "to": 4749, "label": "PARALLEL" }, { "from": 4748, "to": 4750, "label": "PARALLEL" }, { "from": 4749, "to": 4751, "label": "EVAL with clause\nsmall(0).\nand substitutionT1751 -> 0" }, { "from": 4749, "to": 4752, "label": "EVAL-BACKTRACK" }, { "from": 4750, "to": 4755, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1751 -> s(0)" }, { "from": 4750, "to": 4756, "label": "EVAL-BACKTRACK" }, { "from": 4751, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(s(0))))\nT400 -> T1752" }, { "from": 4755, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(s(0))))\nT400 -> T1752" }, { "from": 4758, "to": 4760, "label": "CASE" }, { "from": 4760, "to": 4761, "label": "PARALLEL" }, { "from": 4760, "to": 4762, "label": "PARALLEL" }, { "from": 4761, "to": 4763, "label": "EVAL with clause\nsmall(0).\nand substitutionT1758 -> 0" }, { "from": 4761, "to": 4764, "label": "EVAL-BACKTRACK" }, { "from": 4762, "to": 4768, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1758 -> s(0)" }, { "from": 4762, "to": 4769, "label": "EVAL-BACKTRACK" }, { "from": 4763, "to": 4765, "label": "CASE" }, { "from": 4765, "to": 4766, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4766, "to": 4767, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4768, "to": 4771, "label": "CASE" }, { "from": 4771, "to": 4772, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4772, "to": 4773, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4788, "to": 4820, "label": "ONLY EVAL with clause\nlog2(X3560, s(s(X3561)), X3562, X3563) :- ','(small(X3560), log2(X3561, s(0), s(X3562), X3563)).\nand substitutionT324 -> T1769,\nX3560 -> T1769,\nX3561 -> s(s(s(0))),\nX3562 -> s(s(s(0))),\nT325 -> T1770,\nX3563 -> T1770" }, { "from": 4789, "to": 4833, "label": "EVAL with clause\nlog2(X3582, X3583, X3584, X3584) :- ','(small(X3582), small(X3583)).\nand substitutionT324 -> T1776,\nX3582 -> T1776,\nX3583 -> s(s(s(s(s(0))))),\nX3584 -> s(s(s(0))),\nT325 -> s(s(s(0)))" }, { "from": 4789, "to": 4834, "label": "EVAL-BACKTRACK" }, { "from": 4820, "to": 4821, "label": "CASE" }, { "from": 4821, "to": 4824, "label": "PARALLEL" }, { "from": 4821, "to": 4825, "label": "PARALLEL" }, { "from": 4824, "to": 4826, "label": "EVAL with clause\nsmall(0).\nand substitutionT1769 -> 0" }, { "from": 4824, "to": 4827, "label": "EVAL-BACKTRACK" }, { "from": 4825, "to": 4830, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1769 -> s(0)" }, { "from": 4825, "to": 4831, "label": "EVAL-BACKTRACK" }, { "from": 4826, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(0)))\nT400 -> T1770" }, { "from": 4830, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(s(0)))\nT400 -> T1770" }, { "from": 4833, "to": 4835, "label": "CASE" }, { "from": 4835, "to": 4836, "label": "PARALLEL" }, { "from": 4835, "to": 4837, "label": "PARALLEL" }, { "from": 4836, "to": 4838, "label": "EVAL with clause\nsmall(0).\nand substitutionT1776 -> 0" }, { "from": 4836, "to": 4839, "label": "EVAL-BACKTRACK" }, { "from": 4837, "to": 4843, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1776 -> s(0)" }, { "from": 4837, "to": 4844, "label": "EVAL-BACKTRACK" }, { "from": 4838, "to": 4840, "label": "CASE" }, { "from": 4840, "to": 4841, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4841, "to": 4842, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4843, "to": 4845, "label": "CASE" }, { "from": 4845, "to": 4846, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4846, "to": 4847, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4863, "to": 4895, "label": "ONLY EVAL with clause\nlog2(X3609, s(s(X3610)), X3611, X3612) :- ','(small(X3609), log2(X3610, s(0), s(X3611), X3612)).\nand substitutionT312 -> T1787,\nX3609 -> T1787,\nX3610 -> s(s(0)),\nX3611 -> s(s(s(0))),\nT313 -> T1788,\nX3612 -> T1788" }, { "from": 4864, "to": 4908, "label": "EVAL with clause\nlog2(X3631, X3632, X3633, X3633) :- ','(small(X3631), small(X3632)).\nand substitutionT312 -> T1794,\nX3631 -> T1794,\nX3632 -> s(s(s(s(0)))),\nX3633 -> s(s(s(0))),\nT313 -> s(s(s(0)))" }, { "from": 4864, "to": 4909, "label": "EVAL-BACKTRACK" }, { "from": 4895, "to": 4898, "label": "CASE" }, { "from": 4898, "to": 4899, "label": "PARALLEL" }, { "from": 4898, "to": 4900, "label": "PARALLEL" }, { "from": 4899, "to": 4901, "label": "EVAL with clause\nsmall(0).\nand substitutionT1787 -> 0" }, { "from": 4899, "to": 4902, "label": "EVAL-BACKTRACK" }, { "from": 4900, "to": 4905, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1787 -> s(0)" }, { "from": 4900, "to": 4906, "label": "EVAL-BACKTRACK" }, { "from": 4901, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(0))\nT400 -> T1788" }, { "from": 4905, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(s(0))\nT400 -> T1788" }, { "from": 4908, "to": 4910, "label": "CASE" }, { "from": 4910, "to": 4911, "label": "PARALLEL" }, { "from": 4910, "to": 4912, "label": "PARALLEL" }, { "from": 4911, "to": 4913, "label": "EVAL with clause\nsmall(0).\nand substitutionT1794 -> 0" }, { "from": 4911, "to": 4914, "label": "EVAL-BACKTRACK" }, { "from": 4912, "to": 4918, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1794 -> s(0)" }, { "from": 4912, "to": 4919, "label": "EVAL-BACKTRACK" }, { "from": 4913, "to": 4915, "label": "CASE" }, { "from": 4915, "to": 4916, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4916, "to": 4917, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4918, "to": 4920, "label": "CASE" }, { "from": 4920, "to": 4921, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 4921, "to": 4922, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 4938, "to": 4971, "label": "ONLY EVAL with clause\nlog2(X3658, s(s(X3659)), X3660, X3661) :- ','(small(X3658), log2(X3659, s(0), s(X3660), X3661)).\nand substitutionT300 -> T1803,\nX3658 -> T1803,\nX3659 -> s(0),\nX3660 -> s(s(s(0))),\nT301 -> T1804,\nX3661 -> T1804" }, { "from": 4939, "to": 5000, "label": "EVAL with clause\nlog2(X3680, X3681, X3682, X3682) :- ','(small(X3680), small(X3681)).\nand substitutionT300 -> T1807,\nX3680 -> T1807,\nX3681 -> s(s(s(0))),\nX3682 -> s(s(s(0))),\nT301 -> s(s(s(0)))" }, { "from": 4939, "to": 5001, "label": "EVAL-BACKTRACK" }, { "from": 4971, "to": 4972, "label": "CASE" }, { "from": 4972, "to": 4973, "label": "PARALLEL" }, { "from": 4972, "to": 4974, "label": "PARALLEL" }, { "from": 4973, "to": 4975, "label": "EVAL with clause\nsmall(0).\nand substitutionT1803 -> 0" }, { "from": 4973, "to": 4976, "label": "EVAL-BACKTRACK" }, { "from": 4974, "to": 4996, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1803 -> s(0)" }, { "from": 4974, "to": 4997, "label": "EVAL-BACKTRACK" }, { "from": 4975, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(0)\nT400 -> T1804" }, { "from": 4996, "to": 660, "label": "INSTANCE with matching:\nT399 -> s(0)\nT400 -> T1804" }, { "from": 5000, "to": 5002, "label": "CASE" }, { "from": 5002, "to": 5003, "label": "PARALLEL" }, { "from": 5002, "to": 5004, "label": "PARALLEL" }, { "from": 5003, "to": 5005, "label": "EVAL with clause\nsmall(0).\nand substitutionT1807 -> 0" }, { "from": 5003, "to": 5006, "label": "EVAL-BACKTRACK" }, { "from": 5004, "to": 5010, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1807 -> s(0)" }, { "from": 5004, "to": 5011, "label": "EVAL-BACKTRACK" }, { "from": 5005, "to": 5007, "label": "CASE" }, { "from": 5007, "to": 5008, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5008, "to": 5009, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5010, "to": 5012, "label": "CASE" }, { "from": 5012, "to": 5013, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5013, "to": 5014, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5042, "to": 5061, "label": "ONLY EVAL with clause\nlog2(X3707, s(s(X3708)), X3709, X3710) :- ','(small(X3707), log2(X3708, s(0), s(X3709), X3710)).\nand substitutionT288 -> T1816,\nX3707 -> T1816,\nX3708 -> 0,\nX3709 -> s(s(s(0))),\nT289 -> T1817,\nX3710 -> T1817" }, { "from": 5043, "to": 5097, "label": "EVAL with clause\nlog2(X3729, X3730, X3731, X3731) :- ','(small(X3729), small(X3730)).\nand substitutionT288 -> T1820,\nX3729 -> T1820,\nX3730 -> s(s(0)),\nX3731 -> s(s(s(0))),\nT289 -> s(s(s(0)))" }, { "from": 5043, "to": 5098, "label": "EVAL-BACKTRACK" }, { "from": 5061, "to": 5063, "label": "CASE" }, { "from": 5063, "to": 5064, "label": "PARALLEL" }, { "from": 5063, "to": 5065, "label": "PARALLEL" }, { "from": 5064, "to": 5066, "label": "EVAL with clause\nsmall(0).\nand substitutionT1816 -> 0" }, { "from": 5064, "to": 5067, "label": "EVAL-BACKTRACK" }, { "from": 5065, "to": 5069, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1816 -> s(0)" }, { "from": 5065, "to": 5070, "label": "EVAL-BACKTRACK" }, { "from": 5066, "to": 660, "label": "INSTANCE with matching:\nT399 -> 0\nT400 -> T1817" }, { "from": 5069, "to": 660, "label": "INSTANCE with matching:\nT399 -> 0\nT400 -> T1817" }, { "from": 5097, "to": 5099, "label": "CASE" }, { "from": 5099, "to": 5100, "label": "PARALLEL" }, { "from": 5099, "to": 5101, "label": "PARALLEL" }, { "from": 5100, "to": 5102, "label": "EVAL with clause\nsmall(0).\nand substitutionT1820 -> 0" }, { "from": 5100, "to": 5103, "label": "EVAL-BACKTRACK" }, { "from": 5101, "to": 5107, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1820 -> s(0)" }, { "from": 5101, "to": 5108, "label": "EVAL-BACKTRACK" }, { "from": 5102, "to": 5104, "label": "CASE" }, { "from": 5104, "to": 5105, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5105, "to": 5106, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5107, "to": 5109, "label": "CASE" }, { "from": 5109, "to": 5110, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5110, "to": 5111, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5112, "to": 5147, "label": "EVAL with clause\nlog2(X3742, X3743, X3744, X3744) :- ','(small(X3742), small(X3743)).\nand substitutionT274 -> T1824,\nX3742 -> T1824,\nX3743 -> s(0),\nX3744 -> s(s(s(0))),\nT275 -> s(s(s(0)))" }, { "from": 5112, "to": 5148, "label": "EVAL-BACKTRACK" }, { "from": 5147, "to": 5149, "label": "CASE" }, { "from": 5149, "to": 5150, "label": "PARALLEL" }, { "from": 5149, "to": 5151, "label": "PARALLEL" }, { "from": 5150, "to": 5152, "label": "EVAL with clause\nsmall(0).\nand substitutionT1824 -> 0" }, { "from": 5150, "to": 5153, "label": "EVAL-BACKTRACK" }, { "from": 5151, "to": 5158, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1824 -> s(0)" }, { "from": 5151, "to": 5159, "label": "EVAL-BACKTRACK" }, { "from": 5152, "to": 5154, "label": "CASE" }, { "from": 5154, "to": 5155, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5155, "to": 5156, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5156, "to": 5157, "label": "SUCCESS" }, { "from": 5158, "to": 5160, "label": "CASE" }, { "from": 5160, "to": 5161, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5161, "to": 5162, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5162, "to": 5163, "label": "SUCCESS" }, { "from": 5164, "to": 560, "label": "INSTANCE" }, { "from": 5170, "to": 5172, "label": "CASE" }, { "from": 5172, "to": 5173, "label": "PARALLEL" }, { "from": 5172, "to": 5174, "label": "PARALLEL" }, { "from": 5173, "to": 5175, "label": "EVAL with clause\nsmall(0).\nand substitutionT1831 -> 0" }, { "from": 5173, "to": 5176, "label": "EVAL-BACKTRACK" }, { "from": 5174, "to": 5182, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1831 -> s(0)" }, { "from": 5174, "to": 5183, "label": "EVAL-BACKTRACK" }, { "from": 5175, "to": 5177, "label": "CASE" }, { "from": 5177, "to": 5178, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5178, "to": 5179, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1832 -> 0" }, { "from": 5178, "to": 5180, "label": "EVAL-BACKTRACK" }, { "from": 5179, "to": 5181, "label": "SUCCESS" }, { "from": 5182, "to": 5184, "label": "CASE" }, { "from": 5184, "to": 5185, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5185, "to": 5186, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1832 -> 0" }, { "from": 5185, "to": 5187, "label": "EVAL-BACKTRACK" }, { "from": 5186, "to": 5188, "label": "SUCCESS" }, { "from": 5196, "to": 5210, "label": "ONLY EVAL with clause\nlog2(X3782, s(s(X3783)), X3784, X3785) :- ','(small(X3782), log2(X3783, s(0), s(X3784), X3785)).\nand substitutionT223 -> T1843,\nX3782 -> T1843,\nX3783 -> s(s(s(s(s(0))))),\nX3784 -> s(s(0)),\nT224 -> T1844,\nX3785 -> T1844" }, { "from": 5197, "to": 5249, "label": "EVAL with clause\nlog2(X3804, X3805, X3806, X3806) :- ','(small(X3804), small(X3805)).\nand substitutionT223 -> T1850,\nX3804 -> T1850,\nX3805 -> s(s(s(s(s(s(s(0))))))),\nX3806 -> s(s(0)),\nT224 -> s(s(0))" }, { "from": 5197, "to": 5250, "label": "EVAL-BACKTRACK" }, { "from": 5210, "to": 5238, "label": "CASE" }, { "from": 5238, "to": 5239, "label": "PARALLEL" }, { "from": 5238, "to": 5240, "label": "PARALLEL" }, { "from": 5239, "to": 5241, "label": "EVAL with clause\nsmall(0).\nand substitutionT1843 -> 0" }, { "from": 5239, "to": 5242, "label": "EVAL-BACKTRACK" }, { "from": 5240, "to": 5243, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1843 -> s(0)" }, { "from": 5240, "to": 5244, "label": "EVAL-BACKTRACK" }, { "from": 5241, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(s(s(0)))))\nT275 -> T1844" }, { "from": 5243, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(s(s(0)))))\nT275 -> T1844" }, { "from": 5249, "to": 5251, "label": "CASE" }, { "from": 5251, "to": 5252, "label": "PARALLEL" }, { "from": 5251, "to": 5253, "label": "PARALLEL" }, { "from": 5252, "to": 5254, "label": "EVAL with clause\nsmall(0).\nand substitutionT1850 -> 0" }, { "from": 5252, "to": 5255, "label": "EVAL-BACKTRACK" }, { "from": 5253, "to": 5259, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1850 -> s(0)" }, { "from": 5253, "to": 5260, "label": "EVAL-BACKTRACK" }, { "from": 5254, "to": 5256, "label": "CASE" }, { "from": 5256, "to": 5257, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5257, "to": 5258, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5259, "to": 5261, "label": "CASE" }, { "from": 5261, "to": 5262, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5262, "to": 5263, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5266, "to": 5282, "label": "ONLY EVAL with clause\nlog2(X3831, s(s(X3832)), X3833, X3834) :- ','(small(X3831), log2(X3832, s(0), s(X3833), X3834)).\nand substitutionT211 -> T1861,\nX3831 -> T1861,\nX3832 -> s(s(s(s(0)))),\nX3833 -> s(s(0)),\nT212 -> T1862,\nX3834 -> T1862" }, { "from": 5267, "to": 5324, "label": "EVAL with clause\nlog2(X3853, X3854, X3855, X3855) :- ','(small(X3853), small(X3854)).\nand substitutionT211 -> T1868,\nX3853 -> T1868,\nX3854 -> s(s(s(s(s(s(0)))))),\nX3855 -> s(s(0)),\nT212 -> s(s(0))" }, { "from": 5267, "to": 5325, "label": "EVAL-BACKTRACK" }, { "from": 5282, "to": 5283, "label": "CASE" }, { "from": 5283, "to": 5285, "label": "PARALLEL" }, { "from": 5283, "to": 5286, "label": "PARALLEL" }, { "from": 5285, "to": 5290, "label": "EVAL with clause\nsmall(0).\nand substitutionT1861 -> 0" }, { "from": 5285, "to": 5292, "label": "EVAL-BACKTRACK" }, { "from": 5286, "to": 5318, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1861 -> s(0)" }, { "from": 5286, "to": 5319, "label": "EVAL-BACKTRACK" }, { "from": 5290, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(s(0))))\nT275 -> T1862" }, { "from": 5318, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(s(0))))\nT275 -> T1862" }, { "from": 5324, "to": 5326, "label": "CASE" }, { "from": 5326, "to": 5327, "label": "PARALLEL" }, { "from": 5326, "to": 5328, "label": "PARALLEL" }, { "from": 5327, "to": 5329, "label": "EVAL with clause\nsmall(0).\nand substitutionT1868 -> 0" }, { "from": 5327, "to": 5330, "label": "EVAL-BACKTRACK" }, { "from": 5328, "to": 5334, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1868 -> s(0)" }, { "from": 5328, "to": 5335, "label": "EVAL-BACKTRACK" }, { "from": 5329, "to": 5331, "label": "CASE" }, { "from": 5331, "to": 5332, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5332, "to": 5333, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5334, "to": 5336, "label": "CASE" }, { "from": 5336, "to": 5337, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5337, "to": 5338, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5341, "to": 5357, "label": "ONLY EVAL with clause\nlog2(X3880, s(s(X3881)), X3882, X3883) :- ','(small(X3880), log2(X3881, s(0), s(X3882), X3883)).\nand substitutionT199 -> T1879,\nX3880 -> T1879,\nX3881 -> s(s(s(0))),\nX3882 -> s(s(0)),\nT200 -> T1880,\nX3883 -> T1880" }, { "from": 5342, "to": 5399, "label": "EVAL with clause\nlog2(X3902, X3903, X3904, X3904) :- ','(small(X3902), small(X3903)).\nand substitutionT199 -> T1886,\nX3902 -> T1886,\nX3903 -> s(s(s(s(s(0))))),\nX3904 -> s(s(0)),\nT200 -> s(s(0))" }, { "from": 5342, "to": 5400, "label": "EVAL-BACKTRACK" }, { "from": 5357, "to": 5358, "label": "CASE" }, { "from": 5358, "to": 5359, "label": "PARALLEL" }, { "from": 5358, "to": 5360, "label": "PARALLEL" }, { "from": 5359, "to": 5361, "label": "EVAL with clause\nsmall(0).\nand substitutionT1879 -> 0" }, { "from": 5359, "to": 5362, "label": "EVAL-BACKTRACK" }, { "from": 5360, "to": 5393, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1879 -> s(0)" }, { "from": 5360, "to": 5394, "label": "EVAL-BACKTRACK" }, { "from": 5361, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(0)))\nT275 -> T1880" }, { "from": 5393, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(s(0)))\nT275 -> T1880" }, { "from": 5399, "to": 5401, "label": "CASE" }, { "from": 5401, "to": 5402, "label": "PARALLEL" }, { "from": 5401, "to": 5403, "label": "PARALLEL" }, { "from": 5402, "to": 5404, "label": "EVAL with clause\nsmall(0).\nand substitutionT1886 -> 0" }, { "from": 5402, "to": 5405, "label": "EVAL-BACKTRACK" }, { "from": 5403, "to": 5409, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1886 -> s(0)" }, { "from": 5403, "to": 5410, "label": "EVAL-BACKTRACK" }, { "from": 5404, "to": 5406, "label": "CASE" }, { "from": 5406, "to": 5407, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5407, "to": 5408, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5409, "to": 5411, "label": "CASE" }, { "from": 5411, "to": 5412, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5412, "to": 5413, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5414, "to": 5432, "label": "ONLY EVAL with clause\nlog2(X3929, s(s(X3930)), X3931, X3932) :- ','(small(X3929), log2(X3930, s(0), s(X3931), X3932)).\nand substitutionT187 -> T1897,\nX3929 -> T1897,\nX3930 -> s(s(0)),\nX3931 -> s(s(0)),\nT188 -> T1898,\nX3932 -> T1898" }, { "from": 5415, "to": 5474, "label": "EVAL with clause\nlog2(X3951, X3952, X3953, X3953) :- ','(small(X3951), small(X3952)).\nand substitutionT187 -> T1904,\nX3951 -> T1904,\nX3952 -> s(s(s(s(0)))),\nX3953 -> s(s(0)),\nT188 -> s(s(0))" }, { "from": 5415, "to": 5475, "label": "EVAL-BACKTRACK" }, { "from": 5432, "to": 5433, "label": "CASE" }, { "from": 5433, "to": 5434, "label": "PARALLEL" }, { "from": 5433, "to": 5435, "label": "PARALLEL" }, { "from": 5434, "to": 5436, "label": "EVAL with clause\nsmall(0).\nand substitutionT1897 -> 0" }, { "from": 5434, "to": 5437, "label": "EVAL-BACKTRACK" }, { "from": 5435, "to": 5468, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1897 -> s(0)" }, { "from": 5435, "to": 5469, "label": "EVAL-BACKTRACK" }, { "from": 5436, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(0))\nT275 -> T1898" }, { "from": 5468, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(s(0))\nT275 -> T1898" }, { "from": 5474, "to": 5476, "label": "CASE" }, { "from": 5476, "to": 5477, "label": "PARALLEL" }, { "from": 5476, "to": 5478, "label": "PARALLEL" }, { "from": 5477, "to": 5479, "label": "EVAL with clause\nsmall(0).\nand substitutionT1904 -> 0" }, { "from": 5477, "to": 5480, "label": "EVAL-BACKTRACK" }, { "from": 5478, "to": 5484, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1904 -> s(0)" }, { "from": 5478, "to": 5485, "label": "EVAL-BACKTRACK" }, { "from": 5479, "to": 5481, "label": "CASE" }, { "from": 5481, "to": 5482, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5482, "to": 5483, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5484, "to": 5486, "label": "CASE" }, { "from": 5486, "to": 5487, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5487, "to": 5488, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5489, "to": 5507, "label": "ONLY EVAL with clause\nlog2(X3978, s(s(X3979)), X3980, X3981) :- ','(small(X3978), log2(X3979, s(0), s(X3980), X3981)).\nand substitutionT175 -> T1913,\nX3978 -> T1913,\nX3979 -> s(0),\nX3980 -> s(s(0)),\nT176 -> T1914,\nX3981 -> T1914" }, { "from": 5490, "to": 5567, "label": "EVAL with clause\nlog2(X4000, X4001, X4002, X4002) :- ','(small(X4000), small(X4001)).\nand substitutionT175 -> T1917,\nX4000 -> T1917,\nX4001 -> s(s(s(0))),\nX4002 -> s(s(0)),\nT176 -> s(s(0))" }, { "from": 5490, "to": 5568, "label": "EVAL-BACKTRACK" }, { "from": 5507, "to": 5508, "label": "CASE" }, { "from": 5508, "to": 5509, "label": "PARALLEL" }, { "from": 5508, "to": 5510, "label": "PARALLEL" }, { "from": 5509, "to": 5511, "label": "EVAL with clause\nsmall(0).\nand substitutionT1913 -> 0" }, { "from": 5509, "to": 5512, "label": "EVAL-BACKTRACK" }, { "from": 5510, "to": 5543, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1913 -> s(0)" }, { "from": 5510, "to": 5544, "label": "EVAL-BACKTRACK" }, { "from": 5511, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(0)\nT275 -> T1914" }, { "from": 5543, "to": 560, "label": "INSTANCE with matching:\nT274 -> s(0)\nT275 -> T1914" }, { "from": 5567, "to": 5569, "label": "CASE" }, { "from": 5569, "to": 5570, "label": "PARALLEL" }, { "from": 5569, "to": 5571, "label": "PARALLEL" }, { "from": 5570, "to": 5572, "label": "EVAL with clause\nsmall(0).\nand substitutionT1917 -> 0" }, { "from": 5570, "to": 5573, "label": "EVAL-BACKTRACK" }, { "from": 5571, "to": 5577, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1917 -> s(0)" }, { "from": 5571, "to": 5578, "label": "EVAL-BACKTRACK" }, { "from": 5572, "to": 5574, "label": "CASE" }, { "from": 5574, "to": 5575, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5575, "to": 5576, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5577, "to": 5579, "label": "CASE" }, { "from": 5579, "to": 5580, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5580, "to": 5581, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5607, "to": 5622, "label": "ONLY EVAL with clause\nlog2(X4027, s(s(X4028)), X4029, X4030) :- ','(small(X4027), log2(X4028, s(0), s(X4029), X4030)).\nand substitutionT163 -> T1926,\nX4027 -> T1926,\nX4028 -> 0,\nX4029 -> s(s(0)),\nT164 -> T1927,\nX4030 -> T1927" }, { "from": 5608, "to": 5672, "label": "EVAL with clause\nlog2(X4049, X4050, X4051, X4051) :- ','(small(X4049), small(X4050)).\nand substitutionT163 -> T1930,\nX4049 -> T1930,\nX4050 -> s(s(0)),\nX4051 -> s(s(0)),\nT164 -> s(s(0))" }, { "from": 5608, "to": 5675, "label": "EVAL-BACKTRACK" }, { "from": 5622, "to": 5629, "label": "CASE" }, { "from": 5629, "to": 5630, "label": "PARALLEL" }, { "from": 5629, "to": 5631, "label": "PARALLEL" }, { "from": 5630, "to": 5632, "label": "EVAL with clause\nsmall(0).\nand substitutionT1926 -> 0" }, { "from": 5630, "to": 5633, "label": "EVAL-BACKTRACK" }, { "from": 5631, "to": 5641, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1926 -> s(0)" }, { "from": 5631, "to": 5642, "label": "EVAL-BACKTRACK" }, { "from": 5632, "to": 560, "label": "INSTANCE with matching:\nT274 -> 0\nT275 -> T1927" }, { "from": 5641, "to": 560, "label": "INSTANCE with matching:\nT274 -> 0\nT275 -> T1927" }, { "from": 5672, "to": 5678, "label": "CASE" }, { "from": 5678, "to": 5680, "label": "PARALLEL" }, { "from": 5678, "to": 5681, "label": "PARALLEL" }, { "from": 5680, "to": 5684, "label": "EVAL with clause\nsmall(0).\nand substitutionT1930 -> 0" }, { "from": 5680, "to": 5685, "label": "EVAL-BACKTRACK" }, { "from": 5681, "to": 5689, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1930 -> s(0)" }, { "from": 5681, "to": 5690, "label": "EVAL-BACKTRACK" }, { "from": 5684, "to": 5686, "label": "CASE" }, { "from": 5686, "to": 5687, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5687, "to": 5688, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5689, "to": 5691, "label": "CASE" }, { "from": 5691, "to": 5692, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5692, "to": 5693, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5694, "to": 5716, "label": "EVAL with clause\nlog2(X4062, X4063, X4064, X4064) :- ','(small(X4062), small(X4063)).\nand substitutionT148 -> T1934,\nX4062 -> T1934,\nX4063 -> s(0),\nX4064 -> s(s(0)),\nT149 -> s(s(0))" }, { "from": 5694, "to": 5717, "label": "EVAL-BACKTRACK" }, { "from": 5716, "to": 5718, "label": "CASE" }, { "from": 5718, "to": 5719, "label": "PARALLEL" }, { "from": 5718, "to": 5720, "label": "PARALLEL" }, { "from": 5719, "to": 5721, "label": "EVAL with clause\nsmall(0).\nand substitutionT1934 -> 0" }, { "from": 5719, "to": 5722, "label": "EVAL-BACKTRACK" }, { "from": 5720, "to": 5727, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1934 -> s(0)" }, { "from": 5720, "to": 5728, "label": "EVAL-BACKTRACK" }, { "from": 5721, "to": 5723, "label": "CASE" }, { "from": 5723, "to": 5724, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5724, "to": 5725, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5725, "to": 5726, "label": "SUCCESS" }, { "from": 5727, "to": 5729, "label": "CASE" }, { "from": 5729, "to": 5730, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5730, "to": 5731, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 5731, "to": 5732, "label": "SUCCESS" }, { "from": 5733, "to": 393, "label": "INSTANCE" }, { "from": 5738, "to": 5740, "label": "CASE" }, { "from": 5740, "to": 5741, "label": "PARALLEL" }, { "from": 5740, "to": 5742, "label": "PARALLEL" }, { "from": 5741, "to": 5743, "label": "EVAL with clause\nsmall(0).\nand substitutionT1943 -> 0" }, { "from": 5741, "to": 5744, "label": "EVAL-BACKTRACK" }, { "from": 5742, "to": 5750, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1943 -> s(0)" }, { "from": 5742, "to": 5751, "label": "EVAL-BACKTRACK" }, { "from": 5743, "to": 5745, "label": "CASE" }, { "from": 5745, "to": 5746, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5746, "to": 5747, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1942 -> 0" }, { "from": 5746, "to": 5748, "label": "EVAL-BACKTRACK" }, { "from": 5747, "to": 5749, "label": "SUCCESS" }, { "from": 5750, "to": 5752, "label": "CASE" }, { "from": 5752, "to": 5753, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5753, "to": 5754, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1942 -> 0" }, { "from": 5753, "to": 5756, "label": "EVAL-BACKTRACK" }, { "from": 5754, "to": 5757, "label": "SUCCESS" }, { "from": 5765, "to": 5789, "label": "ONLY EVAL with clause\nlog2(X4102, s(s(X4103)), X4104, X4105) :- ','(small(X4102), log2(X4103, s(0), s(X4104), X4105)).\nand substitutionT96 -> T1958,\nX4102 -> T1958,\nX4103 -> s(s(s(s(s(0))))),\nX4104 -> s(0),\nT95 -> T1957,\nX4105 -> T1957,\nT1956 -> T1958" }, { "from": 5766, "to": 5817, "label": "EVAL with clause\nlog2(X4124, X4125, X4126, X4126) :- ','(small(X4124), small(X4125)).\nand substitutionT96 -> T1965,\nX4124 -> T1965,\nX4125 -> s(s(s(s(s(s(s(0))))))),\nX4126 -> s(0),\nT95 -> s(0),\nT1964 -> T1965" }, { "from": 5766, "to": 5818, "label": "EVAL-BACKTRACK" }, { "from": 5789, "to": 5807, "label": "CASE" }, { "from": 5807, "to": 5808, "label": "PARALLEL" }, { "from": 5807, "to": 5809, "label": "PARALLEL" }, { "from": 5808, "to": 5810, "label": "EVAL with clause\nsmall(0).\nand substitutionT1958 -> 0" }, { "from": 5808, "to": 5811, "label": "EVAL-BACKTRACK" }, { "from": 5809, "to": 5812, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1958 -> s(0)" }, { "from": 5809, "to": 5813, "label": "EVAL-BACKTRACK" }, { "from": 5810, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(s(s(0)))))\nT149 -> T1957" }, { "from": 5812, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(s(s(0)))))\nT149 -> T1957" }, { "from": 5817, "to": 5819, "label": "CASE" }, { "from": 5819, "to": 5820, "label": "PARALLEL" }, { "from": 5819, "to": 5821, "label": "PARALLEL" }, { "from": 5820, "to": 5822, "label": "EVAL with clause\nsmall(0).\nand substitutionT1965 -> 0" }, { "from": 5820, "to": 5823, "label": "EVAL-BACKTRACK" }, { "from": 5821, "to": 5827, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1965 -> s(0)" }, { "from": 5821, "to": 5828, "label": "EVAL-BACKTRACK" }, { "from": 5822, "to": 5824, "label": "CASE" }, { "from": 5824, "to": 5825, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5825, "to": 5826, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5827, "to": 5829, "label": "CASE" }, { "from": 5829, "to": 5830, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5830, "to": 5831, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5839, "to": 5864, "label": "ONLY EVAL with clause\nlog2(X4151, s(s(X4152)), X4153, X4154) :- ','(small(X4151), log2(X4152, s(0), s(X4153), X4154)).\nand substitutionT83 -> T1980,\nX4151 -> T1980,\nX4152 -> s(s(s(s(0)))),\nX4153 -> s(0),\nT82 -> T1979,\nX4154 -> T1979,\nT1978 -> T1980" }, { "from": 5840, "to": 5891, "label": "EVAL with clause\nlog2(X4173, X4174, X4175, X4175) :- ','(small(X4173), small(X4174)).\nand substitutionT83 -> T1987,\nX4173 -> T1987,\nX4174 -> s(s(s(s(s(s(0)))))),\nX4175 -> s(0),\nT82 -> s(0),\nT1986 -> T1987" }, { "from": 5840, "to": 5892, "label": "EVAL-BACKTRACK" }, { "from": 5864, "to": 5865, "label": "CASE" }, { "from": 5865, "to": 5866, "label": "PARALLEL" }, { "from": 5865, "to": 5867, "label": "PARALLEL" }, { "from": 5866, "to": 5868, "label": "EVAL with clause\nsmall(0).\nand substitutionT1980 -> 0" }, { "from": 5866, "to": 5869, "label": "EVAL-BACKTRACK" }, { "from": 5867, "to": 5887, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1980 -> s(0)" }, { "from": 5867, "to": 5888, "label": "EVAL-BACKTRACK" }, { "from": 5868, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(s(0))))\nT149 -> T1979" }, { "from": 5887, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(s(0))))\nT149 -> T1979" }, { "from": 5891, "to": 5893, "label": "CASE" }, { "from": 5893, "to": 5894, "label": "PARALLEL" }, { "from": 5893, "to": 5895, "label": "PARALLEL" }, { "from": 5894, "to": 5896, "label": "EVAL with clause\nsmall(0).\nand substitutionT1987 -> 0" }, { "from": 5894, "to": 5897, "label": "EVAL-BACKTRACK" }, { "from": 5895, "to": 5901, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT1987 -> s(0)" }, { "from": 5895, "to": 5902, "label": "EVAL-BACKTRACK" }, { "from": 5896, "to": 5898, "label": "CASE" }, { "from": 5898, "to": 5899, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5899, "to": 5900, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5901, "to": 5903, "label": "CASE" }, { "from": 5903, "to": 5904, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5904, "to": 5905, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5922, "to": 5954, "label": "ONLY EVAL with clause\nlog2(X4200, s(s(X4201)), X4202, X4203) :- ','(small(X4200), log2(X4201, s(0), s(X4202), X4203)).\nand substitutionT70 -> T2002,\nX4200 -> T2002,\nX4201 -> s(s(s(0))),\nX4202 -> s(0),\nT69 -> T2001,\nX4203 -> T2001,\nT2000 -> T2002" }, { "from": 5923, "to": 5967, "label": "EVAL with clause\nlog2(X4222, X4223, X4224, X4224) :- ','(small(X4222), small(X4223)).\nand substitutionT70 -> T2009,\nX4222 -> T2009,\nX4223 -> s(s(s(s(s(0))))),\nX4224 -> s(0),\nT69 -> s(0),\nT2008 -> T2009" }, { "from": 5923, "to": 5968, "label": "EVAL-BACKTRACK" }, { "from": 5954, "to": 5957, "label": "CASE" }, { "from": 5957, "to": 5958, "label": "PARALLEL" }, { "from": 5957, "to": 5959, "label": "PARALLEL" }, { "from": 5958, "to": 5960, "label": "EVAL with clause\nsmall(0).\nand substitutionT2002 -> 0" }, { "from": 5958, "to": 5961, "label": "EVAL-BACKTRACK" }, { "from": 5959, "to": 5964, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2002 -> s(0)" }, { "from": 5959, "to": 5965, "label": "EVAL-BACKTRACK" }, { "from": 5960, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(0)))\nT149 -> T2001" }, { "from": 5964, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(s(0)))\nT149 -> T2001" }, { "from": 5967, "to": 5969, "label": "CASE" }, { "from": 5969, "to": 5970, "label": "PARALLEL" }, { "from": 5969, "to": 5971, "label": "PARALLEL" }, { "from": 5970, "to": 5972, "label": "EVAL with clause\nsmall(0).\nand substitutionT2009 -> 0" }, { "from": 5970, "to": 5973, "label": "EVAL-BACKTRACK" }, { "from": 5971, "to": 5977, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2009 -> s(0)" }, { "from": 5971, "to": 5978, "label": "EVAL-BACKTRACK" }, { "from": 5972, "to": 5974, "label": "CASE" }, { "from": 5974, "to": 5975, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5975, "to": 5976, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5977, "to": 5979, "label": "CASE" }, { "from": 5979, "to": 5980, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 5980, "to": 5981, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 5997, "to": 6029, "label": "ONLY EVAL with clause\nlog2(X4249, s(s(X4250)), X4251, X4252) :- ','(small(X4249), log2(X4250, s(0), s(X4251), X4252)).\nand substitutionT57 -> T2024,\nX4249 -> T2024,\nX4250 -> s(s(0)),\nX4251 -> s(0),\nT56 -> T2023,\nX4252 -> T2023,\nT2022 -> T2024" }, { "from": 5998, "to": 6042, "label": "EVAL with clause\nlog2(X4271, X4272, X4273, X4273) :- ','(small(X4271), small(X4272)).\nand substitutionT57 -> T2031,\nX4271 -> T2031,\nX4272 -> s(s(s(s(0)))),\nX4273 -> s(0),\nT56 -> s(0),\nT2030 -> T2031" }, { "from": 5998, "to": 6043, "label": "EVAL-BACKTRACK" }, { "from": 6029, "to": 6030, "label": "CASE" }, { "from": 6030, "to": 6031, "label": "PARALLEL" }, { "from": 6030, "to": 6032, "label": "PARALLEL" }, { "from": 6031, "to": 6033, "label": "EVAL with clause\nsmall(0).\nand substitutionT2024 -> 0" }, { "from": 6031, "to": 6034, "label": "EVAL-BACKTRACK" }, { "from": 6032, "to": 6039, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2024 -> s(0)" }, { "from": 6032, "to": 6040, "label": "EVAL-BACKTRACK" }, { "from": 6033, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(0))\nT149 -> T2023" }, { "from": 6039, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(s(0))\nT149 -> T2023" }, { "from": 6042, "to": 6044, "label": "CASE" }, { "from": 6044, "to": 6045, "label": "PARALLEL" }, { "from": 6044, "to": 6046, "label": "PARALLEL" }, { "from": 6045, "to": 6047, "label": "EVAL with clause\nsmall(0).\nand substitutionT2031 -> 0" }, { "from": 6045, "to": 6048, "label": "EVAL-BACKTRACK" }, { "from": 6046, "to": 6052, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2031 -> s(0)" }, { "from": 6046, "to": 6053, "label": "EVAL-BACKTRACK" }, { "from": 6047, "to": 6049, "label": "CASE" }, { "from": 6049, "to": 6050, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6050, "to": 6051, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6052, "to": 6054, "label": "CASE" }, { "from": 6054, "to": 6055, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6055, "to": 6056, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6072, "to": 6104, "label": "ONLY EVAL with clause\nlog2(X4298, s(s(X4299)), X4300, X4301) :- ','(small(X4298), log2(X4299, s(0), s(X4300), X4301)).\nand substitutionT44 -> T2044,\nX4298 -> T2044,\nX4299 -> s(0),\nX4300 -> s(0),\nT43 -> T2043,\nX4301 -> T2043,\nT2042 -> T2044" }, { "from": 6073, "to": 6133, "label": "EVAL with clause\nlog2(X4320, X4321, X4322, X4322) :- ','(small(X4320), small(X4321)).\nand substitutionT44 -> T2048,\nX4320 -> T2048,\nX4321 -> s(s(s(0))),\nX4322 -> s(0),\nT43 -> s(0),\nT2047 -> T2048" }, { "from": 6073, "to": 6134, "label": "EVAL-BACKTRACK" }, { "from": 6104, "to": 6106, "label": "CASE" }, { "from": 6106, "to": 6107, "label": "PARALLEL" }, { "from": 6106, "to": 6108, "label": "PARALLEL" }, { "from": 6107, "to": 6109, "label": "EVAL with clause\nsmall(0).\nand substitutionT2044 -> 0" }, { "from": 6107, "to": 6110, "label": "EVAL-BACKTRACK" }, { "from": 6108, "to": 6113, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2044 -> s(0)" }, { "from": 6108, "to": 6114, "label": "EVAL-BACKTRACK" }, { "from": 6109, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(0)\nT149 -> T2043" }, { "from": 6113, "to": 393, "label": "INSTANCE with matching:\nT148 -> s(0)\nT149 -> T2043" }, { "from": 6133, "to": 6135, "label": "CASE" }, { "from": 6135, "to": 6136, "label": "PARALLEL" }, { "from": 6135, "to": 6137, "label": "PARALLEL" }, { "from": 6136, "to": 6138, "label": "EVAL with clause\nsmall(0).\nand substitutionT2048 -> 0" }, { "from": 6136, "to": 6139, "label": "EVAL-BACKTRACK" }, { "from": 6137, "to": 6143, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2048 -> s(0)" }, { "from": 6137, "to": 6144, "label": "EVAL-BACKTRACK" }, { "from": 6138, "to": 6140, "label": "CASE" }, { "from": 6140, "to": 6141, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6141, "to": 6142, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6143, "to": 6145, "label": "CASE" }, { "from": 6145, "to": 6146, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6146, "to": 6147, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6177, "to": 6195, "label": "ONLY EVAL with clause\nlog2(X4347, s(s(X4348)), X4349, X4350) :- ','(small(X4347), log2(X4348, s(0), s(X4349), X4350)).\nand substitutionT31 -> T2061,\nX4347 -> T2061,\nX4348 -> 0,\nX4349 -> s(0),\nT30 -> T2060,\nX4350 -> T2060,\nT2059 -> T2061" }, { "from": 6178, "to": 6221, "label": "EVAL with clause\nlog2(X4369, X4370, X4371, X4371) :- ','(small(X4369), small(X4370)).\nand substitutionT31 -> T2065,\nX4369 -> T2065,\nX4370 -> s(s(0)),\nX4371 -> s(0),\nT30 -> s(0),\nT2064 -> T2065" }, { "from": 6178, "to": 6222, "label": "EVAL-BACKTRACK" }, { "from": 6195, "to": 6196, "label": "CASE" }, { "from": 6196, "to": 6197, "label": "PARALLEL" }, { "from": 6196, "to": 6198, "label": "PARALLEL" }, { "from": 6197, "to": 6199, "label": "EVAL with clause\nsmall(0).\nand substitutionT2061 -> 0" }, { "from": 6197, "to": 6200, "label": "EVAL-BACKTRACK" }, { "from": 6198, "to": 6207, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2061 -> s(0)" }, { "from": 6198, "to": 6209, "label": "EVAL-BACKTRACK" }, { "from": 6199, "to": 393, "label": "INSTANCE with matching:\nT148 -> 0\nT149 -> T2060" }, { "from": 6207, "to": 393, "label": "INSTANCE with matching:\nT148 -> 0\nT149 -> T2060" }, { "from": 6221, "to": 6223, "label": "CASE" }, { "from": 6223, "to": 6224, "label": "PARALLEL" }, { "from": 6223, "to": 6225, "label": "PARALLEL" }, { "from": 6224, "to": 6226, "label": "EVAL with clause\nsmall(0).\nand substitutionT2065 -> 0" }, { "from": 6224, "to": 6227, "label": "EVAL-BACKTRACK" }, { "from": 6225, "to": 6231, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2065 -> s(0)" }, { "from": 6225, "to": 6232, "label": "EVAL-BACKTRACK" }, { "from": 6226, "to": 6228, "label": "CASE" }, { "from": 6228, "to": 6229, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6229, "to": 6230, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6231, "to": 6233, "label": "CASE" }, { "from": 6233, "to": 6234, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6234, "to": 6235, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6257, "to": 6258, "label": "EVAL with clause\nlog2(X4382, X4383, X4384, X4384) :- ','(small(X4382), small(X4383)).\nand substitutionT18 -> T2070,\nX4382 -> T2070,\nX4383 -> s(0),\nX4384 -> s(0),\nT17 -> s(0),\nT2069 -> T2070" }, { "from": 6257, "to": 6259, "label": "EVAL-BACKTRACK" }, { "from": 6258, "to": 6260, "label": "CASE" }, { "from": 6260, "to": 6261, "label": "PARALLEL" }, { "from": 6260, "to": 6262, "label": "PARALLEL" }, { "from": 6261, "to": 6263, "label": "EVAL with clause\nsmall(0).\nand substitutionT2070 -> 0" }, { "from": 6261, "to": 6264, "label": "EVAL-BACKTRACK" }, { "from": 6262, "to": 6269, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2070 -> s(0)" }, { "from": 6262, "to": 6270, "label": "EVAL-BACKTRACK" }, { "from": 6263, "to": 6265, "label": "CASE" }, { "from": 6265, "to": 6266, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6266, "to": 6267, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 6267, "to": 6268, "label": "SUCCESS" }, { "from": 6269, "to": 6271, "label": "CASE" }, { "from": 6271, "to": 6272, "label": "BACKTRACK\nfor clause: small(0)because of non-unification" }, { "from": 6272, "to": 6273, "label": "ONLY EVAL with clause\nsmall(s(0)).\nand substitution" }, { "from": 6273, "to": 6274, "label": "SUCCESS" }, { "from": 6275, "to": 6276, "label": "EVAL with clause\nlog2(X4395, X4396, X4397, X4397) :- ','(small(X4395), small(X4396)).\nand substitutionT7 -> T2075,\nX4395 -> T2075,\nX4396 -> 0,\nX4397 -> s(0),\nT6 -> s(0),\nT2074 -> T2075" }, { "from": 6275, "to": 6277, "label": "EVAL-BACKTRACK" }, { "from": 6276, "to": 6278, "label": "CASE" }, { "from": 6278, "to": 6279, "label": "PARALLEL" }, { "from": 6278, "to": 6280, "label": "PARALLEL" }, { "from": 6279, "to": 6281, "label": "EVAL with clause\nsmall(0).\nand substitutionT2075 -> 0" }, { "from": 6279, "to": 6282, "label": "EVAL-BACKTRACK" }, { "from": 6280, "to": 6289, "label": "EVAL with clause\nsmall(s(0)).\nand substitutionT2075 -> s(0)" }, { "from": 6280, "to": 6290, "label": "EVAL-BACKTRACK" }, { "from": 6281, "to": 6283, "label": "CASE" }, { "from": 6283, "to": 6284, "label": "PARALLEL" }, { "from": 6283, "to": 6285, "label": "PARALLEL" }, { "from": 6284, "to": 6286, "label": "ONLY EVAL with clause\nsmall(0).\nand substitution" }, { "from": 6285, "to": 6288, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6286, "to": 6287, "label": "SUCCESS" }, { "from": 6289, "to": 6291, "label": "CASE" }, { "from": 6291, "to": 6292, "label": "PARALLEL" }, { "from": 6291, "to": 6293, "label": "PARALLEL" }, { "from": 6292, "to": 6294, "label": "ONLY EVAL with clause\nsmall(0).\nand substitution" }, { "from": 6293, "to": 6296, "label": "BACKTRACK\nfor clause: small(s(0))because of non-unification" }, { "from": 6294, "to": 6295, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (106) Obligation: Triples: log2A(s(s(X1)), X2, X3) :- log2A(X1, s(X2), X3). log2A(0, s(X1), X2) :- log2B(X1, X2). log2A(s(0), s(X1), X2) :- log2B(X1, X2). log2C(s(s(X1)), X2, X3) :- log2C(X1, s(X2), X3). log2C(0, s(X1), X2) :- log2D(X1, X2). log2C(s(0), s(X1), X2) :- log2D(X1, X2). log2E(s(s(X1)), X2, X3) :- log2E(X1, s(X2), X3). log2E(0, s(X1), X2) :- log2F(X1, X2). log2E(s(0), s(X1), X2) :- log2F(X1, X2). log2G(s(s(X1)), X2, X3) :- log2G(X1, s(X2), X3). log2G(0, s(X1), X2) :- log2H(X1, X2). log2G(s(0), s(X1), X2) :- log2H(X1, X2). log2I(s(s(X1)), X2, X3) :- log2I(X1, s(X2), X3). log2I(0, s(X1), X2) :- log2J(X1, X2). log2I(s(0), s(X1), X2) :- log2J(X1, X2). log2K(s(s(X1)), X2, X3) :- log2K(X1, s(X2), X3). log2K(0, s(X1), X2) :- log2L(X1, X2). log2K(s(0), s(X1), X2) :- log2L(X1, X2). log2M(s(s(X1)), X2, X3) :- log2M(X1, s(X2), X3). log2M(0, s(X1), X2) :- log2N(X1, s(s(s(s(s(s(s(0))))))), X2). log2M(s(0), s(X1), X2) :- log2N(X1, s(s(s(s(s(s(s(0))))))), X2). log2O(s(s(X1)), X2, X3, X4) :- log2O(X1, s(X2), X3, X4). log2O(0, s(X1), X2, X3) :- log2N(X1, s(X2), X3). log2O(s(0), s(X1), X2, X3) :- log2N(X1, s(X2), X3). log2N(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) :- log2O(X1, s(s(s(s(s(s(s(0))))))), X2, X3). log2N(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) :- log2N(s(s(s(s(s(0))))), s(X1), X2). log2N(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) :- log2N(s(s(s(s(s(0))))), s(X1), X2). log2N(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) :- log2N(s(s(s(s(0)))), s(X1), X2). log2N(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) :- log2N(s(s(s(s(0)))), s(X1), X2). log2N(s(s(s(s(s(s(s(s(0)))))))), X1, X2) :- log2N(s(s(s(0))), s(X1), X2). log2N(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) :- log2N(s(s(s(0))), s(X1), X2). log2N(s(s(s(s(s(s(0)))))), X1, X2) :- log2N(s(s(0)), s(X1), X2). log2N(s(s(s(s(s(s(s(0))))))), X1, X2) :- log2N(s(s(0)), s(X1), X2). log2N(s(s(s(s(0)))), X1, X2) :- log2N(s(0), s(X1), X2). log2N(s(s(s(s(s(0))))), X1, X2) :- log2N(s(0), s(X1), X2). log2N(s(s(0)), X1, X2) :- log2N(0, s(X1), X2). log2N(s(s(s(0))), X1, X2) :- log2N(0, s(X1), X2). log2L(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2M(X1, s(s(s(s(s(s(s(0))))))), X2). log2L(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2N(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2N(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2N(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2N(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2N(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2N(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(0)))))), X1) :- log2N(s(s(0)), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(s(s(0))))))), X1) :- log2N(s(s(0)), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(0)))), X1) :- log2N(s(0), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(s(s(0))))), X1) :- log2N(s(0), s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(0)), X1) :- log2N(0, s(s(s(s(s(s(s(0))))))), X1). log2L(s(s(s(0))), X1) :- log2N(0, s(s(s(s(s(s(s(0))))))), X1). log2J(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2K(X1, s(s(s(s(s(s(s(0))))))), X2). log2J(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2L(s(s(s(s(s(0))))), X1). log2J(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2L(s(s(s(s(s(0))))), X1). log2J(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2L(s(s(s(s(0)))), X1). log2J(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2L(s(s(s(s(0)))), X1). log2J(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2L(s(s(s(0))), X1). log2J(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2L(s(s(s(0))), X1). log2J(s(s(s(s(s(s(0)))))), X1) :- log2L(s(s(0)), X1). log2J(s(s(s(s(s(s(s(0))))))), X1) :- log2L(s(s(0)), X1). log2J(s(s(s(s(0)))), X1) :- log2L(s(0), X1). log2J(s(s(s(s(s(0))))), X1) :- log2L(s(0), X1). log2J(s(s(0)), X1) :- log2L(0, X1). log2J(s(s(s(0))), X1) :- log2L(0, X1). log2H(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2I(X1, s(s(s(s(s(s(s(0))))))), X2). log2H(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2J(s(s(s(s(s(0))))), X1). log2H(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2J(s(s(s(s(s(0))))), X1). log2H(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2J(s(s(s(s(0)))), X1). log2H(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2J(s(s(s(s(0)))), X1). log2H(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2J(s(s(s(0))), X1). log2H(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2J(s(s(s(0))), X1). log2H(s(s(s(s(s(s(0)))))), X1) :- log2J(s(s(0)), X1). log2H(s(s(s(s(s(s(s(0))))))), X1) :- log2J(s(s(0)), X1). log2H(s(s(s(s(0)))), X1) :- log2J(s(0), X1). log2H(s(s(s(s(s(0))))), X1) :- log2J(s(0), X1). log2H(s(s(0)), X1) :- log2J(0, X1). log2H(s(s(s(0))), X1) :- log2J(0, X1). log2F(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2G(X1, s(s(s(s(s(s(s(0))))))), X2). log2F(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2H(s(s(s(s(s(0))))), X1). log2F(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2H(s(s(s(s(s(0))))), X1). log2F(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2H(s(s(s(s(0)))), X1). log2F(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2H(s(s(s(s(0)))), X1). log2F(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2H(s(s(s(0))), X1). log2F(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2H(s(s(s(0))), X1). log2F(s(s(s(s(s(s(0)))))), X1) :- log2H(s(s(0)), X1). log2F(s(s(s(s(s(s(s(0))))))), X1) :- log2H(s(s(0)), X1). log2F(s(s(s(s(0)))), X1) :- log2H(s(0), X1). log2F(s(s(s(s(s(0))))), X1) :- log2H(s(0), X1). log2F(s(s(0)), X1) :- log2H(0, X1). log2F(s(s(s(0))), X1) :- log2H(0, X1). log2D(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2E(X1, s(s(s(s(s(s(s(0))))))), X2). log2D(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2F(s(s(s(s(s(0))))), X1). log2D(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2F(s(s(s(s(s(0))))), X1). log2D(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2F(s(s(s(s(0)))), X1). log2D(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2F(s(s(s(s(0)))), X1). log2D(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2F(s(s(s(0))), X1). log2D(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2F(s(s(s(0))), X1). log2D(s(s(s(s(s(s(0)))))), X1) :- log2F(s(s(0)), X1). log2D(s(s(s(s(s(s(s(0))))))), X1) :- log2F(s(s(0)), X1). log2D(s(s(s(s(0)))), X1) :- log2F(s(0), X1). log2D(s(s(s(s(s(0))))), X1) :- log2F(s(0), X1). log2D(s(s(0)), X1) :- log2F(0, X1). log2D(s(s(s(0))), X1) :- log2F(0, X1). log2B(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2C(X1, s(s(s(s(s(s(s(0))))))), X2). log2B(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2D(s(s(s(s(s(0))))), X1). log2B(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2D(s(s(s(s(s(0))))), X1). log2B(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2D(s(s(s(s(0)))), X1). log2B(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2D(s(s(s(s(0)))), X1). log2B(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2D(s(s(s(0))), X1). log2B(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2D(s(s(s(0))), X1). log2B(s(s(s(s(s(s(0)))))), X1) :- log2D(s(s(0)), X1). log2B(s(s(s(s(s(s(s(0))))))), X1) :- log2D(s(s(0)), X1). log2B(s(s(s(s(0)))), X1) :- log2D(s(0), X1). log2B(s(s(s(s(s(0))))), X1) :- log2D(s(0), X1). log2B(s(s(0)), X1) :- log2D(0, X1). log2B(s(s(s(0))), X1) :- log2D(0, X1). log2P(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))))), X2) :- log2A(X1, s(s(s(s(s(s(s(0))))))), X2). log2P(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), X1) :- log2B(s(s(s(s(s(0))))), X1). log2P(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), X1) :- log2B(s(s(s(s(s(0))))), X1). log2P(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2B(s(s(s(s(0)))), X1). log2P(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2B(s(s(s(s(0)))), X1). log2P(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2B(s(s(s(0))), X1). log2P(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2B(s(s(s(0))), X1). log2P(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2B(s(s(0)), X1). log2P(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2B(s(s(0)), X1). log2P(s(s(s(s(s(s(0)))))), X1) :- log2B(s(0), X1). log2P(s(s(s(s(s(s(s(0))))))), X1) :- log2B(s(0), X1). log2P(s(s(s(s(0)))), X1) :- log2B(0, X1). log2P(s(s(s(s(s(0))))), X1) :- log2B(0, X1). Clauses: log2cA(s(s(X1)), X2, X3) :- log2cA(X1, s(X2), X3). log2cA(0, s(X1), X2) :- log2cB(X1, X2). log2cA(s(0), s(X1), X2) :- log2cB(X1, X2). log2cA(0, 0, s(0)). log2cA(s(0), 0, s(0)). log2cC(s(s(X1)), X2, X3) :- log2cC(X1, s(X2), X3). log2cC(0, s(X1), X2) :- log2cD(X1, X2). log2cC(s(0), s(X1), X2) :- log2cD(X1, X2). log2cC(0, 0, s(s(0))). log2cC(s(0), 0, s(s(0))). log2cE(s(s(X1)), X2, X3) :- log2cE(X1, s(X2), X3). log2cE(0, s(X1), X2) :- log2cF(X1, X2). log2cE(s(0), s(X1), X2) :- log2cF(X1, X2). log2cE(0, 0, s(s(s(0)))). log2cE(s(0), 0, s(s(s(0)))). log2cG(s(s(X1)), X2, X3) :- log2cG(X1, s(X2), X3). log2cG(0, s(X1), X2) :- log2cH(X1, X2). log2cG(s(0), s(X1), X2) :- log2cH(X1, X2). log2cG(0, 0, s(s(s(s(0))))). log2cG(s(0), 0, s(s(s(s(0))))). log2cI(s(s(X1)), X2, X3) :- log2cI(X1, s(X2), X3). log2cI(0, s(X1), X2) :- log2cJ(X1, X2). log2cI(s(0), s(X1), X2) :- log2cJ(X1, X2). log2cI(0, 0, s(s(s(s(s(0)))))). log2cI(s(0), 0, s(s(s(s(s(0)))))). log2cK(s(s(X1)), X2, X3) :- log2cK(X1, s(X2), X3). log2cK(0, s(X1), X2) :- log2cL(X1, X2). log2cK(s(0), s(X1), X2) :- log2cL(X1, X2). log2cK(0, 0, s(s(s(s(s(s(0))))))). log2cK(s(0), 0, s(s(s(s(s(s(0))))))). log2cM(s(s(X1)), X2, X3) :- log2cM(X1, s(X2), X3). log2cM(0, s(X1), X2) :- log2cN(X1, s(s(s(s(s(s(s(0))))))), X2). log2cM(s(0), s(X1), X2) :- log2cN(X1, s(s(s(s(s(s(s(0))))))), X2). log2cM(0, 0, s(s(s(s(s(s(s(0)))))))). log2cM(s(0), 0, s(s(s(s(s(s(s(0)))))))). log2cO(s(s(X1)), X2, X3, X4) :- log2cO(X1, s(X2), X3, X4). log2cO(0, s(X1), X2, X3) :- log2cN(X1, s(X2), X3). log2cO(s(0), s(X1), X2, X3) :- log2cN(X1, s(X2), X3). log2cO(0, 0, X1, s(X1)). log2cO(s(0), 0, X1, s(X1)). log2cN(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) :- log2cO(X1, s(s(s(s(s(s(s(0))))))), X2, X3). log2cN(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) :- log2cN(s(s(s(s(s(0))))), s(X1), X2). log2cN(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) :- log2cN(s(s(s(s(s(0))))), s(X1), X2). log2cN(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) :- log2cN(s(s(s(s(0)))), s(X1), X2). log2cN(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) :- log2cN(s(s(s(s(0)))), s(X1), X2). log2cN(s(s(s(s(s(s(s(s(0)))))))), X1, X2) :- log2cN(s(s(s(0))), s(X1), X2). log2cN(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) :- log2cN(s(s(s(0))), s(X1), X2). log2cN(s(s(s(s(s(s(0)))))), X1, X2) :- log2cN(s(s(0)), s(X1), X2). log2cN(s(s(s(s(s(s(s(0))))))), X1, X2) :- log2cN(s(s(0)), s(X1), X2). log2cN(s(s(s(s(0)))), X1, X2) :- log2cN(s(0), s(X1), X2). log2cN(s(s(s(s(s(0))))), X1, X2) :- log2cN(s(0), s(X1), X2). log2cN(s(s(0)), X1, X2) :- log2cN(0, s(X1), X2). log2cN(s(s(s(0))), X1, X2) :- log2cN(0, s(X1), X2). log2cN(0, X1, s(X1)). log2cN(s(0), X1, s(X1)). log2cL(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cM(X1, s(s(s(s(s(s(s(0))))))), X2). log2cL(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cN(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cN(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cN(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cN(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cN(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cN(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(0)))))), X1) :- log2cN(s(s(0)), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(s(s(0))))))), X1) :- log2cN(s(s(0)), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(0)))), X1) :- log2cN(s(0), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(s(s(0))))), X1) :- log2cN(s(0), s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(0)), X1) :- log2cN(0, s(s(s(s(s(s(s(0))))))), X1). log2cL(s(s(s(0))), X1) :- log2cN(0, s(s(s(s(s(s(s(0))))))), X1). log2cL(0, s(s(s(s(s(s(s(0)))))))). log2cL(s(0), s(s(s(s(s(s(s(0)))))))). log2cJ(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cK(X1, s(s(s(s(s(s(s(0))))))), X2). log2cJ(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cL(s(s(s(s(s(0))))), X1). log2cJ(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cL(s(s(s(s(s(0))))), X1). log2cJ(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cL(s(s(s(s(0)))), X1). log2cJ(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cL(s(s(s(s(0)))), X1). log2cJ(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cL(s(s(s(0))), X1). log2cJ(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cL(s(s(s(0))), X1). log2cJ(s(s(s(s(s(s(0)))))), X1) :- log2cL(s(s(0)), X1). log2cJ(s(s(s(s(s(s(s(0))))))), X1) :- log2cL(s(s(0)), X1). log2cJ(s(s(s(s(0)))), X1) :- log2cL(s(0), X1). log2cJ(s(s(s(s(s(0))))), X1) :- log2cL(s(0), X1). log2cJ(s(s(0)), X1) :- log2cL(0, X1). log2cJ(s(s(s(0))), X1) :- log2cL(0, X1). log2cJ(0, s(s(s(s(s(s(0))))))). log2cJ(s(0), s(s(s(s(s(s(0))))))). log2cH(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cI(X1, s(s(s(s(s(s(s(0))))))), X2). log2cH(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cJ(s(s(s(s(s(0))))), X1). log2cH(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cJ(s(s(s(s(s(0))))), X1). log2cH(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cJ(s(s(s(s(0)))), X1). log2cH(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cJ(s(s(s(s(0)))), X1). log2cH(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cJ(s(s(s(0))), X1). log2cH(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cJ(s(s(s(0))), X1). log2cH(s(s(s(s(s(s(0)))))), X1) :- log2cJ(s(s(0)), X1). log2cH(s(s(s(s(s(s(s(0))))))), X1) :- log2cJ(s(s(0)), X1). log2cH(s(s(s(s(0)))), X1) :- log2cJ(s(0), X1). log2cH(s(s(s(s(s(0))))), X1) :- log2cJ(s(0), X1). log2cH(s(s(0)), X1) :- log2cJ(0, X1). log2cH(s(s(s(0))), X1) :- log2cJ(0, X1). log2cH(0, s(s(s(s(s(0)))))). log2cH(s(0), s(s(s(s(s(0)))))). log2cF(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cG(X1, s(s(s(s(s(s(s(0))))))), X2). log2cF(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cH(s(s(s(s(s(0))))), X1). log2cF(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cH(s(s(s(s(s(0))))), X1). log2cF(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cH(s(s(s(s(0)))), X1). log2cF(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cH(s(s(s(s(0)))), X1). log2cF(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cH(s(s(s(0))), X1). log2cF(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cH(s(s(s(0))), X1). log2cF(s(s(s(s(s(s(0)))))), X1) :- log2cH(s(s(0)), X1). log2cF(s(s(s(s(s(s(s(0))))))), X1) :- log2cH(s(s(0)), X1). log2cF(s(s(s(s(0)))), X1) :- log2cH(s(0), X1). log2cF(s(s(s(s(s(0))))), X1) :- log2cH(s(0), X1). log2cF(s(s(0)), X1) :- log2cH(0, X1). log2cF(s(s(s(0))), X1) :- log2cH(0, X1). log2cF(0, s(s(s(s(0))))). log2cF(s(0), s(s(s(s(0))))). log2cD(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cE(X1, s(s(s(s(s(s(s(0))))))), X2). log2cD(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cF(s(s(s(s(s(0))))), X1). log2cD(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cF(s(s(s(s(s(0))))), X1). log2cD(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cF(s(s(s(s(0)))), X1). log2cD(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cF(s(s(s(s(0)))), X1). log2cD(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cF(s(s(s(0))), X1). log2cD(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cF(s(s(s(0))), X1). log2cD(s(s(s(s(s(s(0)))))), X1) :- log2cF(s(s(0)), X1). log2cD(s(s(s(s(s(s(s(0))))))), X1) :- log2cF(s(s(0)), X1). log2cD(s(s(s(s(0)))), X1) :- log2cF(s(0), X1). log2cD(s(s(s(s(s(0))))), X1) :- log2cF(s(0), X1). log2cD(s(s(0)), X1) :- log2cF(0, X1). log2cD(s(s(s(0))), X1) :- log2cF(0, X1). log2cD(0, s(s(s(0)))). log2cD(s(0), s(s(s(0)))). log2cB(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) :- log2cC(X1, s(s(s(s(s(s(s(0))))))), X2). log2cB(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) :- log2cD(s(s(s(s(s(0))))), X1). log2cB(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) :- log2cD(s(s(s(s(s(0))))), X1). log2cB(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) :- log2cD(s(s(s(s(0)))), X1). log2cB(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) :- log2cD(s(s(s(s(0)))), X1). log2cB(s(s(s(s(s(s(s(s(0)))))))), X1) :- log2cD(s(s(s(0))), X1). log2cB(s(s(s(s(s(s(s(s(s(0))))))))), X1) :- log2cD(s(s(s(0))), X1). log2cB(s(s(s(s(s(s(0)))))), X1) :- log2cD(s(s(0)), X1). log2cB(s(s(s(s(s(s(s(0))))))), X1) :- log2cD(s(s(0)), X1). log2cB(s(s(s(s(0)))), X1) :- log2cD(s(0), X1). log2cB(s(s(s(s(s(0))))), X1) :- log2cD(s(0), X1). log2cB(s(s(0)), X1) :- log2cD(0, X1). log2cB(s(s(s(0))), X1) :- log2cD(0, X1). log2cB(0, s(s(0))). log2cB(s(0), s(s(0))). Afs: log2P(x1, x2) = log2P(x2) ---------------------------------------- (107) TriplesToPiDPProof (SOUND) We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: log2P_in_2: (f,b) log2A_in_3: (f,b,b) log2B_in_2: (b,b) log2C_in_3: (b,b,b) log2D_in_2: (b,b) log2E_in_3: (b,b,b) log2F_in_2: (b,b) log2G_in_3: (b,b,b) log2H_in_2: (b,b) log2I_in_3: (b,b,b) log2J_in_2: (b,b) log2K_in_3: (b,b,b) log2L_in_2: (b,b) log2M_in_3: (b,b,b) log2N_in_3: (b,b,b) log2O_in_4: (b,b,b,b) Transforming TRIPLES into the following Term Rewriting System: Pi DP problem: The TRS P consists of the following rules: LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))))), X2) -> U116_AG(X1, X2, log2A_in_agg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))))), X2) -> LOG2A_IN_AGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2A_IN_AGG(s(s(X1)), X2, X3) -> U1_AGG(X1, X2, X3, log2A_in_agg(X1, s(X2), X3)) LOG2A_IN_AGG(s(s(X1)), X2, X3) -> LOG2A_IN_AGG(X1, s(X2), X3) LOG2A_IN_AGG(0, s(X1), X2) -> U2_AGG(X1, X2, log2B_in_gg(X1, X2)) LOG2A_IN_AGG(0, s(X1), X2) -> LOG2B_IN_GG(X1, X2) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U103_GG(X1, X2, log2C_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2C_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2C_IN_GGG(s(s(X1)), X2, X3) -> U4_GGG(X1, X2, X3, log2C_in_ggg(X1, s(X2), X3)) LOG2C_IN_GGG(s(s(X1)), X2, X3) -> LOG2C_IN_GGG(X1, s(X2), X3) LOG2C_IN_GGG(0, s(X1), X2) -> U5_GGG(X1, X2, log2D_in_gg(X1, X2)) LOG2C_IN_GGG(0, s(X1), X2) -> LOG2D_IN_GG(X1, X2) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U90_GG(X1, X2, log2E_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2E_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2E_IN_GGG(s(s(X1)), X2, X3) -> U7_GGG(X1, X2, X3, log2E_in_ggg(X1, s(X2), X3)) LOG2E_IN_GGG(s(s(X1)), X2, X3) -> LOG2E_IN_GGG(X1, s(X2), X3) LOG2E_IN_GGG(0, s(X1), X2) -> U8_GGG(X1, X2, log2F_in_gg(X1, X2)) LOG2E_IN_GGG(0, s(X1), X2) -> LOG2F_IN_GG(X1, X2) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U77_GG(X1, X2, log2G_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2G_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2G_IN_GGG(s(s(X1)), X2, X3) -> U10_GGG(X1, X2, X3, log2G_in_ggg(X1, s(X2), X3)) LOG2G_IN_GGG(s(s(X1)), X2, X3) -> LOG2G_IN_GGG(X1, s(X2), X3) LOG2G_IN_GGG(0, s(X1), X2) -> U11_GGG(X1, X2, log2H_in_gg(X1, X2)) LOG2G_IN_GGG(0, s(X1), X2) -> LOG2H_IN_GG(X1, X2) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U64_GG(X1, X2, log2I_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2I_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2I_IN_GGG(s(s(X1)), X2, X3) -> U13_GGG(X1, X2, X3, log2I_in_ggg(X1, s(X2), X3)) LOG2I_IN_GGG(s(s(X1)), X2, X3) -> LOG2I_IN_GGG(X1, s(X2), X3) LOG2I_IN_GGG(0, s(X1), X2) -> U14_GGG(X1, X2, log2J_in_gg(X1, X2)) LOG2I_IN_GGG(0, s(X1), X2) -> LOG2J_IN_GG(X1, X2) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U51_GG(X1, X2, log2K_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2K_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2K_IN_GGG(s(s(X1)), X2, X3) -> U16_GGG(X1, X2, X3, log2K_in_ggg(X1, s(X2), X3)) LOG2K_IN_GGG(s(s(X1)), X2, X3) -> LOG2K_IN_GGG(X1, s(X2), X3) LOG2K_IN_GGG(0, s(X1), X2) -> U17_GGG(X1, X2, log2L_in_gg(X1, X2)) LOG2K_IN_GGG(0, s(X1), X2) -> LOG2L_IN_GG(X1, X2) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U38_GG(X1, X2, log2M_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2M_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2M_IN_GGG(s(s(X1)), X2, X3) -> U19_GGG(X1, X2, X3, log2M_in_ggg(X1, s(X2), X3)) LOG2M_IN_GGG(s(s(X1)), X2, X3) -> LOG2M_IN_GGG(X1, s(X2), X3) LOG2M_IN_GGG(0, s(X1), X2) -> U20_GGG(X1, X2, log2N_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2M_IN_GGG(0, s(X1), X2) -> LOG2N_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> U25_GGG(X1, X2, X3, log2O_in_gggg(X1, s(s(s(s(s(s(s(0))))))), X2, X3)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> LOG2O_IN_GGGG(X1, s(s(s(s(s(s(s(0))))))), X2, X3) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> U22_GGGG(X1, X2, X3, X4, log2O_in_gggg(X1, s(X2), X3, X4)) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> LOG2O_IN_GGGG(X1, s(X2), X3, X4) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> U23_GGGG(X1, X2, X3, log2N_in_ggg(X1, s(X2), X3)) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) -> U26_GGG(X1, X2, log2N_in_ggg(s(s(s(s(s(0))))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) -> U27_GGG(X1, X2, log2N_in_ggg(s(s(s(s(s(0))))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) -> U28_GGG(X1, X2, log2N_in_ggg(s(s(s(s(0)))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) -> U29_GGG(X1, X2, log2N_in_ggg(s(s(s(s(0)))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), X1, X2) -> U30_GGG(X1, X2, log2N_in_ggg(s(s(s(0))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(0))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) -> U31_GGG(X1, X2, log2N_in_ggg(s(s(s(0))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(0))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(0)))))), X1, X2) -> U32_GGG(X1, X2, log2N_in_ggg(s(s(0)), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(0)))))), X1, X2) -> LOG2N_IN_GGG(s(s(0)), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(0))))))), X1, X2) -> U33_GGG(X1, X2, log2N_in_ggg(s(s(0)), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(0))))))), X1, X2) -> LOG2N_IN_GGG(s(s(0)), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(0)))), X1, X2) -> U34_GGG(X1, X2, log2N_in_ggg(s(0), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(0)))), X1, X2) -> LOG2N_IN_GGG(s(0), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(0))))), X1, X2) -> U35_GGG(X1, X2, log2N_in_ggg(s(0), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(0))))), X1, X2) -> LOG2N_IN_GGG(s(0), s(X1), X2) LOG2N_IN_GGG(s(s(0)), X1, X2) -> U36_GGG(X1, X2, log2N_in_ggg(0, s(X1), X2)) LOG2N_IN_GGG(s(s(0)), X1, X2) -> LOG2N_IN_GGG(0, s(X1), X2) LOG2N_IN_GGG(s(s(s(0))), X1, X2) -> U37_GGG(X1, X2, log2N_in_ggg(0, s(X1), X2)) LOG2N_IN_GGG(s(s(s(0))), X1, X2) -> LOG2N_IN_GGG(0, s(X1), X2) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> U24_GGGG(X1, X2, X3, log2N_in_ggg(X1, s(X2), X3)) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2M_IN_GGG(s(0), s(X1), X2) -> U21_GGG(X1, X2, log2N_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2M_IN_GGG(s(0), s(X1), X2) -> LOG2N_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U39_GG(X1, log2N_in_ggg(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U40_GG(X1, log2N_in_ggg(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U41_GG(X1, log2N_in_ggg(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U42_GG(X1, log2N_in_ggg(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U43_GG(X1, log2N_in_ggg(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2N_IN_GGG(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U44_GG(X1, log2N_in_ggg(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2N_IN_GGG(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U45_GG(X1, log2N_in_ggg(s(s(0)), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2N_IN_GGG(s(s(0)), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U46_GG(X1, log2N_in_ggg(s(s(0)), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2N_IN_GGG(s(s(0)), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(0)))), X1) -> U47_GG(X1, log2N_in_ggg(s(0), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(0)))), X1) -> LOG2N_IN_GGG(s(0), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(0))))), X1) -> U48_GG(X1, log2N_in_ggg(s(0), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2N_IN_GGG(s(0), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(0)), X1) -> U49_GG(X1, log2N_in_ggg(0, s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(0)), X1) -> LOG2N_IN_GGG(0, s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(0))), X1) -> U50_GG(X1, log2N_in_ggg(0, s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(0))), X1) -> LOG2N_IN_GGG(0, s(s(s(s(s(s(s(0))))))), X1) LOG2K_IN_GGG(s(0), s(X1), X2) -> U18_GGG(X1, X2, log2L_in_gg(X1, X2)) LOG2K_IN_GGG(s(0), s(X1), X2) -> LOG2L_IN_GG(X1, X2) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U52_GG(X1, log2L_in_gg(s(s(s(s(s(0))))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(s(0))))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U53_GG(X1, log2L_in_gg(s(s(s(s(s(0))))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(s(0))))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U54_GG(X1, log2L_in_gg(s(s(s(s(0)))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(0)))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U55_GG(X1, log2L_in_gg(s(s(s(s(0)))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(0)))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U56_GG(X1, log2L_in_gg(s(s(s(0))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2L_IN_GG(s(s(s(0))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U57_GG(X1, log2L_in_gg(s(s(s(0))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2L_IN_GG(s(s(s(0))), X1) LOG2J_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U58_GG(X1, log2L_in_gg(s(s(0)), X1)) LOG2J_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2L_IN_GG(s(s(0)), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U59_GG(X1, log2L_in_gg(s(s(0)), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2L_IN_GG(s(s(0)), X1) LOG2J_IN_GG(s(s(s(s(0)))), X1) -> U60_GG(X1, log2L_in_gg(s(0), X1)) LOG2J_IN_GG(s(s(s(s(0)))), X1) -> LOG2L_IN_GG(s(0), X1) LOG2J_IN_GG(s(s(s(s(s(0))))), X1) -> U61_GG(X1, log2L_in_gg(s(0), X1)) LOG2J_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2L_IN_GG(s(0), X1) LOG2J_IN_GG(s(s(0)), X1) -> U62_GG(X1, log2L_in_gg(0, X1)) LOG2J_IN_GG(s(s(0)), X1) -> LOG2L_IN_GG(0, X1) LOG2J_IN_GG(s(s(s(0))), X1) -> U63_GG(X1, log2L_in_gg(0, X1)) LOG2J_IN_GG(s(s(s(0))), X1) -> LOG2L_IN_GG(0, X1) LOG2I_IN_GGG(s(0), s(X1), X2) -> U15_GGG(X1, X2, log2J_in_gg(X1, X2)) LOG2I_IN_GGG(s(0), s(X1), X2) -> LOG2J_IN_GG(X1, X2) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U65_GG(X1, log2J_in_gg(s(s(s(s(s(0))))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(s(0))))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U66_GG(X1, log2J_in_gg(s(s(s(s(s(0))))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(s(0))))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U67_GG(X1, log2J_in_gg(s(s(s(s(0)))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(0)))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U68_GG(X1, log2J_in_gg(s(s(s(s(0)))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(0)))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U69_GG(X1, log2J_in_gg(s(s(s(0))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2J_IN_GG(s(s(s(0))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U70_GG(X1, log2J_in_gg(s(s(s(0))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2J_IN_GG(s(s(s(0))), X1) LOG2H_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U71_GG(X1, log2J_in_gg(s(s(0)), X1)) LOG2H_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2J_IN_GG(s(s(0)), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U72_GG(X1, log2J_in_gg(s(s(0)), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2J_IN_GG(s(s(0)), X1) LOG2H_IN_GG(s(s(s(s(0)))), X1) -> U73_GG(X1, log2J_in_gg(s(0), X1)) LOG2H_IN_GG(s(s(s(s(0)))), X1) -> LOG2J_IN_GG(s(0), X1) LOG2H_IN_GG(s(s(s(s(s(0))))), X1) -> U74_GG(X1, log2J_in_gg(s(0), X1)) LOG2H_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2J_IN_GG(s(0), X1) LOG2H_IN_GG(s(s(0)), X1) -> U75_GG(X1, log2J_in_gg(0, X1)) LOG2H_IN_GG(s(s(0)), X1) -> LOG2J_IN_GG(0, X1) LOG2H_IN_GG(s(s(s(0))), X1) -> U76_GG(X1, log2J_in_gg(0, X1)) LOG2H_IN_GG(s(s(s(0))), X1) -> LOG2J_IN_GG(0, X1) LOG2G_IN_GGG(s(0), s(X1), X2) -> U12_GGG(X1, X2, log2H_in_gg(X1, X2)) LOG2G_IN_GGG(s(0), s(X1), X2) -> LOG2H_IN_GG(X1, X2) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U78_GG(X1, log2H_in_gg(s(s(s(s(s(0))))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(s(0))))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U79_GG(X1, log2H_in_gg(s(s(s(s(s(0))))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(s(0))))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U80_GG(X1, log2H_in_gg(s(s(s(s(0)))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(0)))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U81_GG(X1, log2H_in_gg(s(s(s(s(0)))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(0)))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U82_GG(X1, log2H_in_gg(s(s(s(0))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2H_IN_GG(s(s(s(0))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U83_GG(X1, log2H_in_gg(s(s(s(0))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2H_IN_GG(s(s(s(0))), X1) LOG2F_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U84_GG(X1, log2H_in_gg(s(s(0)), X1)) LOG2F_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2H_IN_GG(s(s(0)), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U85_GG(X1, log2H_in_gg(s(s(0)), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2H_IN_GG(s(s(0)), X1) LOG2F_IN_GG(s(s(s(s(0)))), X1) -> U86_GG(X1, log2H_in_gg(s(0), X1)) LOG2F_IN_GG(s(s(s(s(0)))), X1) -> LOG2H_IN_GG(s(0), X1) LOG2F_IN_GG(s(s(s(s(s(0))))), X1) -> U87_GG(X1, log2H_in_gg(s(0), X1)) LOG2F_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2H_IN_GG(s(0), X1) LOG2F_IN_GG(s(s(0)), X1) -> U88_GG(X1, log2H_in_gg(0, X1)) LOG2F_IN_GG(s(s(0)), X1) -> LOG2H_IN_GG(0, X1) LOG2F_IN_GG(s(s(s(0))), X1) -> U89_GG(X1, log2H_in_gg(0, X1)) LOG2F_IN_GG(s(s(s(0))), X1) -> LOG2H_IN_GG(0, X1) LOG2E_IN_GGG(s(0), s(X1), X2) -> U9_GGG(X1, X2, log2F_in_gg(X1, X2)) LOG2E_IN_GGG(s(0), s(X1), X2) -> LOG2F_IN_GG(X1, X2) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U91_GG(X1, log2F_in_gg(s(s(s(s(s(0))))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(s(0))))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U92_GG(X1, log2F_in_gg(s(s(s(s(s(0))))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(s(0))))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U93_GG(X1, log2F_in_gg(s(s(s(s(0)))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(0)))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U94_GG(X1, log2F_in_gg(s(s(s(s(0)))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(0)))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U95_GG(X1, log2F_in_gg(s(s(s(0))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2F_IN_GG(s(s(s(0))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U96_GG(X1, log2F_in_gg(s(s(s(0))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2F_IN_GG(s(s(s(0))), X1) LOG2D_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U97_GG(X1, log2F_in_gg(s(s(0)), X1)) LOG2D_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2F_IN_GG(s(s(0)), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U98_GG(X1, log2F_in_gg(s(s(0)), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2F_IN_GG(s(s(0)), X1) LOG2D_IN_GG(s(s(s(s(0)))), X1) -> U99_GG(X1, log2F_in_gg(s(0), X1)) LOG2D_IN_GG(s(s(s(s(0)))), X1) -> LOG2F_IN_GG(s(0), X1) LOG2D_IN_GG(s(s(s(s(s(0))))), X1) -> U100_GG(X1, log2F_in_gg(s(0), X1)) LOG2D_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2F_IN_GG(s(0), X1) LOG2D_IN_GG(s(s(0)), X1) -> U101_GG(X1, log2F_in_gg(0, X1)) LOG2D_IN_GG(s(s(0)), X1) -> LOG2F_IN_GG(0, X1) LOG2D_IN_GG(s(s(s(0))), X1) -> U102_GG(X1, log2F_in_gg(0, X1)) LOG2D_IN_GG(s(s(s(0))), X1) -> LOG2F_IN_GG(0, X1) LOG2C_IN_GGG(s(0), s(X1), X2) -> U6_GGG(X1, X2, log2D_in_gg(X1, X2)) LOG2C_IN_GGG(s(0), s(X1), X2) -> LOG2D_IN_GG(X1, X2) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U104_GG(X1, log2D_in_gg(s(s(s(s(s(0))))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(s(0))))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U105_GG(X1, log2D_in_gg(s(s(s(s(s(0))))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(s(0))))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U106_GG(X1, log2D_in_gg(s(s(s(s(0)))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(0)))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U107_GG(X1, log2D_in_gg(s(s(s(s(0)))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(0)))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U108_GG(X1, log2D_in_gg(s(s(s(0))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2D_IN_GG(s(s(s(0))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U109_GG(X1, log2D_in_gg(s(s(s(0))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2D_IN_GG(s(s(s(0))), X1) LOG2B_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U110_GG(X1, log2D_in_gg(s(s(0)), X1)) LOG2B_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2D_IN_GG(s(s(0)), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U111_GG(X1, log2D_in_gg(s(s(0)), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2D_IN_GG(s(s(0)), X1) LOG2B_IN_GG(s(s(s(s(0)))), X1) -> U112_GG(X1, log2D_in_gg(s(0), X1)) LOG2B_IN_GG(s(s(s(s(0)))), X1) -> LOG2D_IN_GG(s(0), X1) LOG2B_IN_GG(s(s(s(s(s(0))))), X1) -> U113_GG(X1, log2D_in_gg(s(0), X1)) LOG2B_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2D_IN_GG(s(0), X1) LOG2B_IN_GG(s(s(0)), X1) -> U114_GG(X1, log2D_in_gg(0, X1)) LOG2B_IN_GG(s(s(0)), X1) -> LOG2D_IN_GG(0, X1) LOG2B_IN_GG(s(s(s(0))), X1) -> U115_GG(X1, log2D_in_gg(0, X1)) LOG2B_IN_GG(s(s(s(0))), X1) -> LOG2D_IN_GG(0, X1) LOG2A_IN_AGG(s(0), s(X1), X2) -> U3_AGG(X1, X2, log2B_in_gg(X1, X2)) LOG2A_IN_AGG(s(0), s(X1), X2) -> LOG2B_IN_GG(X1, X2) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), X1) -> U117_AG(X1, log2B_in_gg(s(s(s(s(s(0))))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(s(0))))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), X1) -> U118_AG(X1, log2B_in_gg(s(s(s(s(s(0))))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(s(0))))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U119_AG(X1, log2B_in_gg(s(s(s(s(0)))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(0)))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U120_AG(X1, log2B_in_gg(s(s(s(s(0)))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(0)))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U121_AG(X1, log2B_in_gg(s(s(s(0))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2B_IN_GG(s(s(s(0))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U122_AG(X1, log2B_in_gg(s(s(s(0))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2B_IN_GG(s(s(s(0))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U123_AG(X1, log2B_in_gg(s(s(0)), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2B_IN_GG(s(s(0)), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U124_AG(X1, log2B_in_gg(s(s(0)), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2B_IN_GG(s(s(0)), X1) LOG2P_IN_AG(s(s(s(s(s(s(0)))))), X1) -> U125_AG(X1, log2B_in_gg(s(0), X1)) LOG2P_IN_AG(s(s(s(s(s(s(0)))))), X1) -> LOG2B_IN_GG(s(0), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(0))))))), X1) -> U126_AG(X1, log2B_in_gg(s(0), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2B_IN_GG(s(0), X1) LOG2P_IN_AG(s(s(s(s(0)))), X1) -> U127_AG(X1, log2B_in_gg(0, X1)) LOG2P_IN_AG(s(s(s(s(0)))), X1) -> LOG2B_IN_GG(0, X1) LOG2P_IN_AG(s(s(s(s(s(0))))), X1) -> U128_AG(X1, log2B_in_gg(0, X1)) LOG2P_IN_AG(s(s(s(s(s(0))))), X1) -> LOG2B_IN_GG(0, X1) R is empty. The argument filtering Pi contains the following mapping: log2A_in_agg(x1, x2, x3) = log2A_in_agg(x2, x3) s(x1) = s(x1) log2B_in_gg(x1, x2) = log2B_in_gg(x1, x2) log2C_in_ggg(x1, x2, x3) = log2C_in_ggg(x1, x2, x3) 0 = 0 log2D_in_gg(x1, x2) = log2D_in_gg(x1, x2) log2E_in_ggg(x1, x2, x3) = log2E_in_ggg(x1, x2, x3) log2F_in_gg(x1, x2) = log2F_in_gg(x1, x2) log2G_in_ggg(x1, x2, x3) = log2G_in_ggg(x1, x2, x3) log2H_in_gg(x1, x2) = log2H_in_gg(x1, x2) log2I_in_ggg(x1, x2, x3) = log2I_in_ggg(x1, x2, x3) log2J_in_gg(x1, x2) = log2J_in_gg(x1, x2) log2K_in_ggg(x1, x2, x3) = log2K_in_ggg(x1, x2, x3) log2L_in_gg(x1, x2) = log2L_in_gg(x1, x2) log2M_in_ggg(x1, x2, x3) = log2M_in_ggg(x1, x2, x3) log2N_in_ggg(x1, x2, x3) = log2N_in_ggg(x1, x2, x3) log2O_in_gggg(x1, x2, x3, x4) = log2O_in_gggg(x1, x2, x3, x4) LOG2P_IN_AG(x1, x2) = LOG2P_IN_AG(x2) U116_AG(x1, x2, x3) = U116_AG(x2, x3) LOG2A_IN_AGG(x1, x2, x3) = LOG2A_IN_AGG(x2, x3) U1_AGG(x1, x2, x3, x4) = U1_AGG(x2, x3, x4) U2_AGG(x1, x2, x3) = U2_AGG(x1, x2, x3) LOG2B_IN_GG(x1, x2) = LOG2B_IN_GG(x1, x2) U103_GG(x1, x2, x3) = U103_GG(x1, x2, x3) LOG2C_IN_GGG(x1, x2, x3) = LOG2C_IN_GGG(x1, x2, x3) U4_GGG(x1, x2, x3, x4) = U4_GGG(x1, x2, x3, x4) U5_GGG(x1, x2, x3) = U5_GGG(x1, x2, x3) LOG2D_IN_GG(x1, x2) = LOG2D_IN_GG(x1, x2) U90_GG(x1, x2, x3) = U90_GG(x1, x2, x3) LOG2E_IN_GGG(x1, x2, x3) = LOG2E_IN_GGG(x1, x2, x3) U7_GGG(x1, x2, x3, x4) = U7_GGG(x1, x2, x3, x4) U8_GGG(x1, x2, x3) = U8_GGG(x1, x2, x3) LOG2F_IN_GG(x1, x2) = LOG2F_IN_GG(x1, x2) U77_GG(x1, x2, x3) = U77_GG(x1, x2, x3) LOG2G_IN_GGG(x1, x2, x3) = LOG2G_IN_GGG(x1, x2, x3) U10_GGG(x1, x2, x3, x4) = U10_GGG(x1, x2, x3, x4) U11_GGG(x1, x2, x3) = U11_GGG(x1, x2, x3) LOG2H_IN_GG(x1, x2) = LOG2H_IN_GG(x1, x2) U64_GG(x1, x2, x3) = U64_GG(x1, x2, x3) LOG2I_IN_GGG(x1, x2, x3) = LOG2I_IN_GGG(x1, x2, x3) U13_GGG(x1, x2, x3, x4) = U13_GGG(x1, x2, x3, x4) U14_GGG(x1, x2, x3) = U14_GGG(x1, x2, x3) LOG2J_IN_GG(x1, x2) = LOG2J_IN_GG(x1, x2) U51_GG(x1, x2, x3) = U51_GG(x1, x2, x3) LOG2K_IN_GGG(x1, x2, x3) = LOG2K_IN_GGG(x1, x2, x3) U16_GGG(x1, x2, x3, x4) = U16_GGG(x1, x2, x3, x4) U17_GGG(x1, x2, x3) = U17_GGG(x1, x2, x3) LOG2L_IN_GG(x1, x2) = LOG2L_IN_GG(x1, x2) U38_GG(x1, x2, x3) = U38_GG(x1, x2, x3) LOG2M_IN_GGG(x1, x2, x3) = LOG2M_IN_GGG(x1, x2, x3) U19_GGG(x1, x2, x3, x4) = U19_GGG(x1, x2, x3, x4) U20_GGG(x1, x2, x3) = U20_GGG(x1, x2, x3) LOG2N_IN_GGG(x1, x2, x3) = LOG2N_IN_GGG(x1, x2, x3) U25_GGG(x1, x2, x3, x4) = U25_GGG(x1, x2, x3, x4) LOG2O_IN_GGGG(x1, x2, x3, x4) = LOG2O_IN_GGGG(x1, x2, x3, x4) U22_GGGG(x1, x2, x3, x4, x5) = U22_GGGG(x1, x2, x3, x4, x5) U23_GGGG(x1, x2, x3, x4) = U23_GGGG(x1, x2, x3, x4) U26_GGG(x1, x2, x3) = U26_GGG(x1, x2, x3) U27_GGG(x1, x2, x3) = U27_GGG(x1, x2, x3) U28_GGG(x1, x2, x3) = U28_GGG(x1, x2, x3) U29_GGG(x1, x2, x3) = U29_GGG(x1, x2, x3) U30_GGG(x1, x2, x3) = U30_GGG(x1, x2, x3) U31_GGG(x1, x2, x3) = U31_GGG(x1, x2, x3) U32_GGG(x1, x2, x3) = U32_GGG(x1, x2, x3) U33_GGG(x1, x2, x3) = U33_GGG(x1, x2, x3) U34_GGG(x1, x2, x3) = U34_GGG(x1, x2, x3) U35_GGG(x1, x2, x3) = U35_GGG(x1, x2, x3) U36_GGG(x1, x2, x3) = U36_GGG(x1, x2, x3) U37_GGG(x1, x2, x3) = U37_GGG(x1, x2, x3) U24_GGGG(x1, x2, x3, x4) = U24_GGGG(x1, x2, x3, x4) U21_GGG(x1, x2, x3) = U21_GGG(x1, x2, x3) U39_GG(x1, x2) = U39_GG(x1, x2) U40_GG(x1, x2) = U40_GG(x1, x2) U41_GG(x1, x2) = U41_GG(x1, x2) U42_GG(x1, x2) = U42_GG(x1, x2) U43_GG(x1, x2) = U43_GG(x1, x2) U44_GG(x1, x2) = U44_GG(x1, x2) U45_GG(x1, x2) = U45_GG(x1, x2) U46_GG(x1, x2) = U46_GG(x1, x2) U47_GG(x1, x2) = U47_GG(x1, x2) U48_GG(x1, x2) = U48_GG(x1, x2) U49_GG(x1, x2) = U49_GG(x1, x2) U50_GG(x1, x2) = U50_GG(x1, x2) U18_GGG(x1, x2, x3) = U18_GGG(x1, x2, x3) U52_GG(x1, x2) = U52_GG(x1, x2) U53_GG(x1, x2) = U53_GG(x1, x2) U54_GG(x1, x2) = U54_GG(x1, x2) U55_GG(x1, x2) = U55_GG(x1, x2) U56_GG(x1, x2) = U56_GG(x1, x2) U57_GG(x1, x2) = U57_GG(x1, x2) U58_GG(x1, x2) = U58_GG(x1, x2) U59_GG(x1, x2) = U59_GG(x1, x2) U60_GG(x1, x2) = U60_GG(x1, x2) U61_GG(x1, x2) = U61_GG(x1, x2) U62_GG(x1, x2) = U62_GG(x1, x2) U63_GG(x1, x2) = U63_GG(x1, x2) U15_GGG(x1, x2, x3) = U15_GGG(x1, x2, x3) U65_GG(x1, x2) = U65_GG(x1, x2) U66_GG(x1, x2) = U66_GG(x1, x2) U67_GG(x1, x2) = U67_GG(x1, x2) U68_GG(x1, x2) = U68_GG(x1, x2) U69_GG(x1, x2) = U69_GG(x1, x2) U70_GG(x1, x2) = U70_GG(x1, x2) U71_GG(x1, x2) = U71_GG(x1, x2) U72_GG(x1, x2) = U72_GG(x1, x2) U73_GG(x1, x2) = U73_GG(x1, x2) U74_GG(x1, x2) = U74_GG(x1, x2) U75_GG(x1, x2) = U75_GG(x1, x2) U76_GG(x1, x2) = U76_GG(x1, x2) U12_GGG(x1, x2, x3) = U12_GGG(x1, x2, x3) U78_GG(x1, x2) = U78_GG(x1, x2) U79_GG(x1, x2) = U79_GG(x1, x2) U80_GG(x1, x2) = U80_GG(x1, x2) U81_GG(x1, x2) = U81_GG(x1, x2) U82_GG(x1, x2) = U82_GG(x1, x2) U83_GG(x1, x2) = U83_GG(x1, x2) U84_GG(x1, x2) = U84_GG(x1, x2) U85_GG(x1, x2) = U85_GG(x1, x2) U86_GG(x1, x2) = U86_GG(x1, x2) U87_GG(x1, x2) = U87_GG(x1, x2) U88_GG(x1, x2) = U88_GG(x1, x2) U89_GG(x1, x2) = U89_GG(x1, x2) U9_GGG(x1, x2, x3) = U9_GGG(x1, x2, x3) U91_GG(x1, x2) = U91_GG(x1, x2) U92_GG(x1, x2) = U92_GG(x1, x2) U93_GG(x1, x2) = U93_GG(x1, x2) U94_GG(x1, x2) = U94_GG(x1, x2) U95_GG(x1, x2) = U95_GG(x1, x2) U96_GG(x1, x2) = U96_GG(x1, x2) U97_GG(x1, x2) = U97_GG(x1, x2) U98_GG(x1, x2) = U98_GG(x1, x2) U99_GG(x1, x2) = U99_GG(x1, x2) U100_GG(x1, x2) = U100_GG(x1, x2) U101_GG(x1, x2) = U101_GG(x1, x2) U102_GG(x1, x2) = U102_GG(x1, x2) U6_GGG(x1, x2, x3) = U6_GGG(x1, x2, x3) U104_GG(x1, x2) = U104_GG(x1, x2) U105_GG(x1, x2) = U105_GG(x1, x2) U106_GG(x1, x2) = U106_GG(x1, x2) U107_GG(x1, x2) = U107_GG(x1, x2) U108_GG(x1, x2) = U108_GG(x1, x2) U109_GG(x1, x2) = U109_GG(x1, x2) U110_GG(x1, x2) = U110_GG(x1, x2) U111_GG(x1, x2) = U111_GG(x1, x2) U112_GG(x1, x2) = U112_GG(x1, x2) U113_GG(x1, x2) = U113_GG(x1, x2) U114_GG(x1, x2) = U114_GG(x1, x2) U115_GG(x1, x2) = U115_GG(x1, x2) U3_AGG(x1, x2, x3) = U3_AGG(x1, x2, x3) U117_AG(x1, x2) = U117_AG(x1, x2) U118_AG(x1, x2) = U118_AG(x1, x2) U119_AG(x1, x2) = U119_AG(x1, x2) U120_AG(x1, x2) = U120_AG(x1, x2) U121_AG(x1, x2) = U121_AG(x1, x2) U122_AG(x1, x2) = U122_AG(x1, x2) U123_AG(x1, x2) = U123_AG(x1, x2) U124_AG(x1, x2) = U124_AG(x1, x2) U125_AG(x1, x2) = U125_AG(x1, x2) U126_AG(x1, x2) = U126_AG(x1, x2) U127_AG(x1, x2) = U127_AG(x1, x2) U128_AG(x1, x2) = U128_AG(x1, x2) We have to consider all (P,R,Pi)-chains Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES ---------------------------------------- (108) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))))), X2) -> U116_AG(X1, X2, log2A_in_agg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))))), X2) -> LOG2A_IN_AGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2A_IN_AGG(s(s(X1)), X2, X3) -> U1_AGG(X1, X2, X3, log2A_in_agg(X1, s(X2), X3)) LOG2A_IN_AGG(s(s(X1)), X2, X3) -> LOG2A_IN_AGG(X1, s(X2), X3) LOG2A_IN_AGG(0, s(X1), X2) -> U2_AGG(X1, X2, log2B_in_gg(X1, X2)) LOG2A_IN_AGG(0, s(X1), X2) -> LOG2B_IN_GG(X1, X2) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U103_GG(X1, X2, log2C_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2C_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2C_IN_GGG(s(s(X1)), X2, X3) -> U4_GGG(X1, X2, X3, log2C_in_ggg(X1, s(X2), X3)) LOG2C_IN_GGG(s(s(X1)), X2, X3) -> LOG2C_IN_GGG(X1, s(X2), X3) LOG2C_IN_GGG(0, s(X1), X2) -> U5_GGG(X1, X2, log2D_in_gg(X1, X2)) LOG2C_IN_GGG(0, s(X1), X2) -> LOG2D_IN_GG(X1, X2) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U90_GG(X1, X2, log2E_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2E_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2E_IN_GGG(s(s(X1)), X2, X3) -> U7_GGG(X1, X2, X3, log2E_in_ggg(X1, s(X2), X3)) LOG2E_IN_GGG(s(s(X1)), X2, X3) -> LOG2E_IN_GGG(X1, s(X2), X3) LOG2E_IN_GGG(0, s(X1), X2) -> U8_GGG(X1, X2, log2F_in_gg(X1, X2)) LOG2E_IN_GGG(0, s(X1), X2) -> LOG2F_IN_GG(X1, X2) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U77_GG(X1, X2, log2G_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2G_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2G_IN_GGG(s(s(X1)), X2, X3) -> U10_GGG(X1, X2, X3, log2G_in_ggg(X1, s(X2), X3)) LOG2G_IN_GGG(s(s(X1)), X2, X3) -> LOG2G_IN_GGG(X1, s(X2), X3) LOG2G_IN_GGG(0, s(X1), X2) -> U11_GGG(X1, X2, log2H_in_gg(X1, X2)) LOG2G_IN_GGG(0, s(X1), X2) -> LOG2H_IN_GG(X1, X2) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U64_GG(X1, X2, log2I_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2I_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2I_IN_GGG(s(s(X1)), X2, X3) -> U13_GGG(X1, X2, X3, log2I_in_ggg(X1, s(X2), X3)) LOG2I_IN_GGG(s(s(X1)), X2, X3) -> LOG2I_IN_GGG(X1, s(X2), X3) LOG2I_IN_GGG(0, s(X1), X2) -> U14_GGG(X1, X2, log2J_in_gg(X1, X2)) LOG2I_IN_GGG(0, s(X1), X2) -> LOG2J_IN_GG(X1, X2) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U51_GG(X1, X2, log2K_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2K_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2K_IN_GGG(s(s(X1)), X2, X3) -> U16_GGG(X1, X2, X3, log2K_in_ggg(X1, s(X2), X3)) LOG2K_IN_GGG(s(s(X1)), X2, X3) -> LOG2K_IN_GGG(X1, s(X2), X3) LOG2K_IN_GGG(0, s(X1), X2) -> U17_GGG(X1, X2, log2L_in_gg(X1, X2)) LOG2K_IN_GGG(0, s(X1), X2) -> LOG2L_IN_GG(X1, X2) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> U38_GG(X1, X2, log2M_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2) -> LOG2M_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2M_IN_GGG(s(s(X1)), X2, X3) -> U19_GGG(X1, X2, X3, log2M_in_ggg(X1, s(X2), X3)) LOG2M_IN_GGG(s(s(X1)), X2, X3) -> LOG2M_IN_GGG(X1, s(X2), X3) LOG2M_IN_GGG(0, s(X1), X2) -> U20_GGG(X1, X2, log2N_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2M_IN_GGG(0, s(X1), X2) -> LOG2N_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> U25_GGG(X1, X2, X3, log2O_in_gggg(X1, s(s(s(s(s(s(s(0))))))), X2, X3)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> LOG2O_IN_GGGG(X1, s(s(s(s(s(s(s(0))))))), X2, X3) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> U22_GGGG(X1, X2, X3, X4, log2O_in_gggg(X1, s(X2), X3, X4)) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> LOG2O_IN_GGGG(X1, s(X2), X3, X4) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> U23_GGGG(X1, X2, X3, log2N_in_ggg(X1, s(X2), X3)) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) -> U26_GGG(X1, X2, log2N_in_ggg(s(s(s(s(s(0))))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) -> U27_GGG(X1, X2, log2N_in_ggg(s(s(s(s(s(0))))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) -> U28_GGG(X1, X2, log2N_in_ggg(s(s(s(s(0)))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) -> U29_GGG(X1, X2, log2N_in_ggg(s(s(s(s(0)))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), X1, X2) -> U30_GGG(X1, X2, log2N_in_ggg(s(s(s(0))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(0)))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(0))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) -> U31_GGG(X1, X2, log2N_in_ggg(s(s(s(0))), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(0))))))))), X1, X2) -> LOG2N_IN_GGG(s(s(s(0))), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(0)))))), X1, X2) -> U32_GGG(X1, X2, log2N_in_ggg(s(s(0)), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(0)))))), X1, X2) -> LOG2N_IN_GGG(s(s(0)), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(s(s(0))))))), X1, X2) -> U33_GGG(X1, X2, log2N_in_ggg(s(s(0)), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(s(s(0))))))), X1, X2) -> LOG2N_IN_GGG(s(s(0)), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(0)))), X1, X2) -> U34_GGG(X1, X2, log2N_in_ggg(s(0), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(0)))), X1, X2) -> LOG2N_IN_GGG(s(0), s(X1), X2) LOG2N_IN_GGG(s(s(s(s(s(0))))), X1, X2) -> U35_GGG(X1, X2, log2N_in_ggg(s(0), s(X1), X2)) LOG2N_IN_GGG(s(s(s(s(s(0))))), X1, X2) -> LOG2N_IN_GGG(s(0), s(X1), X2) LOG2N_IN_GGG(s(s(0)), X1, X2) -> U36_GGG(X1, X2, log2N_in_ggg(0, s(X1), X2)) LOG2N_IN_GGG(s(s(0)), X1, X2) -> LOG2N_IN_GGG(0, s(X1), X2) LOG2N_IN_GGG(s(s(s(0))), X1, X2) -> U37_GGG(X1, X2, log2N_in_ggg(0, s(X1), X2)) LOG2N_IN_GGG(s(s(s(0))), X1, X2) -> LOG2N_IN_GGG(0, s(X1), X2) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> U24_GGGG(X1, X2, X3, log2N_in_ggg(X1, s(X2), X3)) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2M_IN_GGG(s(0), s(X1), X2) -> U21_GGG(X1, X2, log2N_in_ggg(X1, s(s(s(s(s(s(s(0))))))), X2)) LOG2M_IN_GGG(s(0), s(X1), X2) -> LOG2N_IN_GGG(X1, s(s(s(s(s(s(s(0))))))), X2) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U39_GG(X1, log2N_in_ggg(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U40_GG(X1, log2N_in_ggg(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U41_GG(X1, log2N_in_ggg(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U42_GG(X1, log2N_in_ggg(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2N_IN_GGG(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U43_GG(X1, log2N_in_ggg(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2N_IN_GGG(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U44_GG(X1, log2N_in_ggg(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2N_IN_GGG(s(s(s(0))), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U45_GG(X1, log2N_in_ggg(s(s(0)), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2N_IN_GGG(s(s(0)), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U46_GG(X1, log2N_in_ggg(s(s(0)), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2N_IN_GGG(s(s(0)), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(0)))), X1) -> U47_GG(X1, log2N_in_ggg(s(0), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(0)))), X1) -> LOG2N_IN_GGG(s(0), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(s(s(0))))), X1) -> U48_GG(X1, log2N_in_ggg(s(0), s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2N_IN_GGG(s(0), s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(0)), X1) -> U49_GG(X1, log2N_in_ggg(0, s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(0)), X1) -> LOG2N_IN_GGG(0, s(s(s(s(s(s(s(0))))))), X1) LOG2L_IN_GG(s(s(s(0))), X1) -> U50_GG(X1, log2N_in_ggg(0, s(s(s(s(s(s(s(0))))))), X1)) LOG2L_IN_GG(s(s(s(0))), X1) -> LOG2N_IN_GGG(0, s(s(s(s(s(s(s(0))))))), X1) LOG2K_IN_GGG(s(0), s(X1), X2) -> U18_GGG(X1, X2, log2L_in_gg(X1, X2)) LOG2K_IN_GGG(s(0), s(X1), X2) -> LOG2L_IN_GG(X1, X2) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U52_GG(X1, log2L_in_gg(s(s(s(s(s(0))))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(s(0))))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U53_GG(X1, log2L_in_gg(s(s(s(s(s(0))))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(s(0))))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U54_GG(X1, log2L_in_gg(s(s(s(s(0)))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(0)))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U55_GG(X1, log2L_in_gg(s(s(s(s(0)))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2L_IN_GG(s(s(s(s(0)))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U56_GG(X1, log2L_in_gg(s(s(s(0))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2L_IN_GG(s(s(s(0))), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U57_GG(X1, log2L_in_gg(s(s(s(0))), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2L_IN_GG(s(s(s(0))), X1) LOG2J_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U58_GG(X1, log2L_in_gg(s(s(0)), X1)) LOG2J_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2L_IN_GG(s(s(0)), X1) LOG2J_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U59_GG(X1, log2L_in_gg(s(s(0)), X1)) LOG2J_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2L_IN_GG(s(s(0)), X1) LOG2J_IN_GG(s(s(s(s(0)))), X1) -> U60_GG(X1, log2L_in_gg(s(0), X1)) LOG2J_IN_GG(s(s(s(s(0)))), X1) -> LOG2L_IN_GG(s(0), X1) LOG2J_IN_GG(s(s(s(s(s(0))))), X1) -> U61_GG(X1, log2L_in_gg(s(0), X1)) LOG2J_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2L_IN_GG(s(0), X1) LOG2J_IN_GG(s(s(0)), X1) -> U62_GG(X1, log2L_in_gg(0, X1)) LOG2J_IN_GG(s(s(0)), X1) -> LOG2L_IN_GG(0, X1) LOG2J_IN_GG(s(s(s(0))), X1) -> U63_GG(X1, log2L_in_gg(0, X1)) LOG2J_IN_GG(s(s(s(0))), X1) -> LOG2L_IN_GG(0, X1) LOG2I_IN_GGG(s(0), s(X1), X2) -> U15_GGG(X1, X2, log2J_in_gg(X1, X2)) LOG2I_IN_GGG(s(0), s(X1), X2) -> LOG2J_IN_GG(X1, X2) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U65_GG(X1, log2J_in_gg(s(s(s(s(s(0))))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(s(0))))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U66_GG(X1, log2J_in_gg(s(s(s(s(s(0))))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(s(0))))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U67_GG(X1, log2J_in_gg(s(s(s(s(0)))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(0)))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U68_GG(X1, log2J_in_gg(s(s(s(s(0)))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2J_IN_GG(s(s(s(s(0)))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U69_GG(X1, log2J_in_gg(s(s(s(0))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2J_IN_GG(s(s(s(0))), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U70_GG(X1, log2J_in_gg(s(s(s(0))), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2J_IN_GG(s(s(s(0))), X1) LOG2H_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U71_GG(X1, log2J_in_gg(s(s(0)), X1)) LOG2H_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2J_IN_GG(s(s(0)), X1) LOG2H_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U72_GG(X1, log2J_in_gg(s(s(0)), X1)) LOG2H_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2J_IN_GG(s(s(0)), X1) LOG2H_IN_GG(s(s(s(s(0)))), X1) -> U73_GG(X1, log2J_in_gg(s(0), X1)) LOG2H_IN_GG(s(s(s(s(0)))), X1) -> LOG2J_IN_GG(s(0), X1) LOG2H_IN_GG(s(s(s(s(s(0))))), X1) -> U74_GG(X1, log2J_in_gg(s(0), X1)) LOG2H_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2J_IN_GG(s(0), X1) LOG2H_IN_GG(s(s(0)), X1) -> U75_GG(X1, log2J_in_gg(0, X1)) LOG2H_IN_GG(s(s(0)), X1) -> LOG2J_IN_GG(0, X1) LOG2H_IN_GG(s(s(s(0))), X1) -> U76_GG(X1, log2J_in_gg(0, X1)) LOG2H_IN_GG(s(s(s(0))), X1) -> LOG2J_IN_GG(0, X1) LOG2G_IN_GGG(s(0), s(X1), X2) -> U12_GGG(X1, X2, log2H_in_gg(X1, X2)) LOG2G_IN_GGG(s(0), s(X1), X2) -> LOG2H_IN_GG(X1, X2) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U78_GG(X1, log2H_in_gg(s(s(s(s(s(0))))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(s(0))))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U79_GG(X1, log2H_in_gg(s(s(s(s(s(0))))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(s(0))))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U80_GG(X1, log2H_in_gg(s(s(s(s(0)))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(0)))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U81_GG(X1, log2H_in_gg(s(s(s(s(0)))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2H_IN_GG(s(s(s(s(0)))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U82_GG(X1, log2H_in_gg(s(s(s(0))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2H_IN_GG(s(s(s(0))), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U83_GG(X1, log2H_in_gg(s(s(s(0))), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2H_IN_GG(s(s(s(0))), X1) LOG2F_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U84_GG(X1, log2H_in_gg(s(s(0)), X1)) LOG2F_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2H_IN_GG(s(s(0)), X1) LOG2F_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U85_GG(X1, log2H_in_gg(s(s(0)), X1)) LOG2F_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2H_IN_GG(s(s(0)), X1) LOG2F_IN_GG(s(s(s(s(0)))), X1) -> U86_GG(X1, log2H_in_gg(s(0), X1)) LOG2F_IN_GG(s(s(s(s(0)))), X1) -> LOG2H_IN_GG(s(0), X1) LOG2F_IN_GG(s(s(s(s(s(0))))), X1) -> U87_GG(X1, log2H_in_gg(s(0), X1)) LOG2F_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2H_IN_GG(s(0), X1) LOG2F_IN_GG(s(s(0)), X1) -> U88_GG(X1, log2H_in_gg(0, X1)) LOG2F_IN_GG(s(s(0)), X1) -> LOG2H_IN_GG(0, X1) LOG2F_IN_GG(s(s(s(0))), X1) -> U89_GG(X1, log2H_in_gg(0, X1)) LOG2F_IN_GG(s(s(s(0))), X1) -> LOG2H_IN_GG(0, X1) LOG2E_IN_GGG(s(0), s(X1), X2) -> U9_GGG(X1, X2, log2F_in_gg(X1, X2)) LOG2E_IN_GGG(s(0), s(X1), X2) -> LOG2F_IN_GG(X1, X2) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U91_GG(X1, log2F_in_gg(s(s(s(s(s(0))))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(s(0))))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U92_GG(X1, log2F_in_gg(s(s(s(s(s(0))))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(s(0))))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U93_GG(X1, log2F_in_gg(s(s(s(s(0)))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(0)))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U94_GG(X1, log2F_in_gg(s(s(s(s(0)))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2F_IN_GG(s(s(s(s(0)))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U95_GG(X1, log2F_in_gg(s(s(s(0))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2F_IN_GG(s(s(s(0))), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U96_GG(X1, log2F_in_gg(s(s(s(0))), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2F_IN_GG(s(s(s(0))), X1) LOG2D_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U97_GG(X1, log2F_in_gg(s(s(0)), X1)) LOG2D_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2F_IN_GG(s(s(0)), X1) LOG2D_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U98_GG(X1, log2F_in_gg(s(s(0)), X1)) LOG2D_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2F_IN_GG(s(s(0)), X1) LOG2D_IN_GG(s(s(s(s(0)))), X1) -> U99_GG(X1, log2F_in_gg(s(0), X1)) LOG2D_IN_GG(s(s(s(s(0)))), X1) -> LOG2F_IN_GG(s(0), X1) LOG2D_IN_GG(s(s(s(s(s(0))))), X1) -> U100_GG(X1, log2F_in_gg(s(0), X1)) LOG2D_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2F_IN_GG(s(0), X1) LOG2D_IN_GG(s(s(0)), X1) -> U101_GG(X1, log2F_in_gg(0, X1)) LOG2D_IN_GG(s(s(0)), X1) -> LOG2F_IN_GG(0, X1) LOG2D_IN_GG(s(s(s(0))), X1) -> U102_GG(X1, log2F_in_gg(0, X1)) LOG2D_IN_GG(s(s(s(0))), X1) -> LOG2F_IN_GG(0, X1) LOG2C_IN_GGG(s(0), s(X1), X2) -> U6_GGG(X1, X2, log2D_in_gg(X1, X2)) LOG2C_IN_GGG(s(0), s(X1), X2) -> LOG2D_IN_GG(X1, X2) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U104_GG(X1, log2D_in_gg(s(s(s(s(s(0))))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(s(0))))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U105_GG(X1, log2D_in_gg(s(s(s(s(s(0))))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(s(0))))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U106_GG(X1, log2D_in_gg(s(s(s(s(0)))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(0)))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U107_GG(X1, log2D_in_gg(s(s(s(s(0)))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2D_IN_GG(s(s(s(s(0)))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U108_GG(X1, log2D_in_gg(s(s(s(0))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2D_IN_GG(s(s(s(0))), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U109_GG(X1, log2D_in_gg(s(s(s(0))), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2D_IN_GG(s(s(s(0))), X1) LOG2B_IN_GG(s(s(s(s(s(s(0)))))), X1) -> U110_GG(X1, log2D_in_gg(s(s(0)), X1)) LOG2B_IN_GG(s(s(s(s(s(s(0)))))), X1) -> LOG2D_IN_GG(s(s(0)), X1) LOG2B_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> U111_GG(X1, log2D_in_gg(s(s(0)), X1)) LOG2B_IN_GG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2D_IN_GG(s(s(0)), X1) LOG2B_IN_GG(s(s(s(s(0)))), X1) -> U112_GG(X1, log2D_in_gg(s(0), X1)) LOG2B_IN_GG(s(s(s(s(0)))), X1) -> LOG2D_IN_GG(s(0), X1) LOG2B_IN_GG(s(s(s(s(s(0))))), X1) -> U113_GG(X1, log2D_in_gg(s(0), X1)) LOG2B_IN_GG(s(s(s(s(s(0))))), X1) -> LOG2D_IN_GG(s(0), X1) LOG2B_IN_GG(s(s(0)), X1) -> U114_GG(X1, log2D_in_gg(0, X1)) LOG2B_IN_GG(s(s(0)), X1) -> LOG2D_IN_GG(0, X1) LOG2B_IN_GG(s(s(s(0))), X1) -> U115_GG(X1, log2D_in_gg(0, X1)) LOG2B_IN_GG(s(s(s(0))), X1) -> LOG2D_IN_GG(0, X1) LOG2A_IN_AGG(s(0), s(X1), X2) -> U3_AGG(X1, X2, log2B_in_gg(X1, X2)) LOG2A_IN_AGG(s(0), s(X1), X2) -> LOG2B_IN_GG(X1, X2) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), X1) -> U117_AG(X1, log2B_in_gg(s(s(s(s(s(0))))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(s(0))))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), X1) -> U118_AG(X1, log2B_in_gg(s(s(s(s(s(0))))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(s(0))))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> U119_AG(X1, log2B_in_gg(s(s(s(s(0)))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(0)))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(0)))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> U120_AG(X1, log2B_in_gg(s(s(s(s(0)))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))), X1) -> LOG2B_IN_GG(s(s(s(s(0)))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> U121_AG(X1, log2B_in_gg(s(s(s(0))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(0)))))))))), X1) -> LOG2B_IN_GG(s(s(s(0))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> U122_AG(X1, log2B_in_gg(s(s(s(0))), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(s(s(0))))))))))), X1) -> LOG2B_IN_GG(s(s(s(0))), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(0)))))))), X1) -> U123_AG(X1, log2B_in_gg(s(s(0)), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(0)))))))), X1) -> LOG2B_IN_GG(s(s(0)), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> U124_AG(X1, log2B_in_gg(s(s(0)), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(s(s(0))))))))), X1) -> LOG2B_IN_GG(s(s(0)), X1) LOG2P_IN_AG(s(s(s(s(s(s(0)))))), X1) -> U125_AG(X1, log2B_in_gg(s(0), X1)) LOG2P_IN_AG(s(s(s(s(s(s(0)))))), X1) -> LOG2B_IN_GG(s(0), X1) LOG2P_IN_AG(s(s(s(s(s(s(s(0))))))), X1) -> U126_AG(X1, log2B_in_gg(s(0), X1)) LOG2P_IN_AG(s(s(s(s(s(s(s(0))))))), X1) -> LOG2B_IN_GG(s(0), X1) LOG2P_IN_AG(s(s(s(s(0)))), X1) -> U127_AG(X1, log2B_in_gg(0, X1)) LOG2P_IN_AG(s(s(s(s(0)))), X1) -> LOG2B_IN_GG(0, X1) LOG2P_IN_AG(s(s(s(s(s(0))))), X1) -> U128_AG(X1, log2B_in_gg(0, X1)) LOG2P_IN_AG(s(s(s(s(s(0))))), X1) -> LOG2B_IN_GG(0, X1) R is empty. The argument filtering Pi contains the following mapping: log2A_in_agg(x1, x2, x3) = log2A_in_agg(x2, x3) s(x1) = s(x1) log2B_in_gg(x1, x2) = log2B_in_gg(x1, x2) log2C_in_ggg(x1, x2, x3) = log2C_in_ggg(x1, x2, x3) 0 = 0 log2D_in_gg(x1, x2) = log2D_in_gg(x1, x2) log2E_in_ggg(x1, x2, x3) = log2E_in_ggg(x1, x2, x3) log2F_in_gg(x1, x2) = log2F_in_gg(x1, x2) log2G_in_ggg(x1, x2, x3) = log2G_in_ggg(x1, x2, x3) log2H_in_gg(x1, x2) = log2H_in_gg(x1, x2) log2I_in_ggg(x1, x2, x3) = log2I_in_ggg(x1, x2, x3) log2J_in_gg(x1, x2) = log2J_in_gg(x1, x2) log2K_in_ggg(x1, x2, x3) = log2K_in_ggg(x1, x2, x3) log2L_in_gg(x1, x2) = log2L_in_gg(x1, x2) log2M_in_ggg(x1, x2, x3) = log2M_in_ggg(x1, x2, x3) log2N_in_ggg(x1, x2, x3) = log2N_in_ggg(x1, x2, x3) log2O_in_gggg(x1, x2, x3, x4) = log2O_in_gggg(x1, x2, x3, x4) LOG2P_IN_AG(x1, x2) = LOG2P_IN_AG(x2) U116_AG(x1, x2, x3) = U116_AG(x2, x3) LOG2A_IN_AGG(x1, x2, x3) = LOG2A_IN_AGG(x2, x3) U1_AGG(x1, x2, x3, x4) = U1_AGG(x2, x3, x4) U2_AGG(x1, x2, x3) = U2_AGG(x1, x2, x3) LOG2B_IN_GG(x1, x2) = LOG2B_IN_GG(x1, x2) U103_GG(x1, x2, x3) = U103_GG(x1, x2, x3) LOG2C_IN_GGG(x1, x2, x3) = LOG2C_IN_GGG(x1, x2, x3) U4_GGG(x1, x2, x3, x4) = U4_GGG(x1, x2, x3, x4) U5_GGG(x1, x2, x3) = U5_GGG(x1, x2, x3) LOG2D_IN_GG(x1, x2) = LOG2D_IN_GG(x1, x2) U90_GG(x1, x2, x3) = U90_GG(x1, x2, x3) LOG2E_IN_GGG(x1, x2, x3) = LOG2E_IN_GGG(x1, x2, x3) U7_GGG(x1, x2, x3, x4) = U7_GGG(x1, x2, x3, x4) U8_GGG(x1, x2, x3) = U8_GGG(x1, x2, x3) LOG2F_IN_GG(x1, x2) = LOG2F_IN_GG(x1, x2) U77_GG(x1, x2, x3) = U77_GG(x1, x2, x3) LOG2G_IN_GGG(x1, x2, x3) = LOG2G_IN_GGG(x1, x2, x3) U10_GGG(x1, x2, x3, x4) = U10_GGG(x1, x2, x3, x4) U11_GGG(x1, x2, x3) = U11_GGG(x1, x2, x3) LOG2H_IN_GG(x1, x2) = LOG2H_IN_GG(x1, x2) U64_GG(x1, x2, x3) = U64_GG(x1, x2, x3) LOG2I_IN_GGG(x1, x2, x3) = LOG2I_IN_GGG(x1, x2, x3) U13_GGG(x1, x2, x3, x4) = U13_GGG(x1, x2, x3, x4) U14_GGG(x1, x2, x3) = U14_GGG(x1, x2, x3) LOG2J_IN_GG(x1, x2) = LOG2J_IN_GG(x1, x2) U51_GG(x1, x2, x3) = U51_GG(x1, x2, x3) LOG2K_IN_GGG(x1, x2, x3) = LOG2K_IN_GGG(x1, x2, x3) U16_GGG(x1, x2, x3, x4) = U16_GGG(x1, x2, x3, x4) U17_GGG(x1, x2, x3) = U17_GGG(x1, x2, x3) LOG2L_IN_GG(x1, x2) = LOG2L_IN_GG(x1, x2) U38_GG(x1, x2, x3) = U38_GG(x1, x2, x3) LOG2M_IN_GGG(x1, x2, x3) = LOG2M_IN_GGG(x1, x2, x3) U19_GGG(x1, x2, x3, x4) = U19_GGG(x1, x2, x3, x4) U20_GGG(x1, x2, x3) = U20_GGG(x1, x2, x3) LOG2N_IN_GGG(x1, x2, x3) = LOG2N_IN_GGG(x1, x2, x3) U25_GGG(x1, x2, x3, x4) = U25_GGG(x1, x2, x3, x4) LOG2O_IN_GGGG(x1, x2, x3, x4) = LOG2O_IN_GGGG(x1, x2, x3, x4) U22_GGGG(x1, x2, x3, x4, x5) = U22_GGGG(x1, x2, x3, x4, x5) U23_GGGG(x1, x2, x3, x4) = U23_GGGG(x1, x2, x3, x4) U26_GGG(x1, x2, x3) = U26_GGG(x1, x2, x3) U27_GGG(x1, x2, x3) = U27_GGG(x1, x2, x3) U28_GGG(x1, x2, x3) = U28_GGG(x1, x2, x3) U29_GGG(x1, x2, x3) = U29_GGG(x1, x2, x3) U30_GGG(x1, x2, x3) = U30_GGG(x1, x2, x3) U31_GGG(x1, x2, x3) = U31_GGG(x1, x2, x3) U32_GGG(x1, x2, x3) = U32_GGG(x1, x2, x3) U33_GGG(x1, x2, x3) = U33_GGG(x1, x2, x3) U34_GGG(x1, x2, x3) = U34_GGG(x1, x2, x3) U35_GGG(x1, x2, x3) = U35_GGG(x1, x2, x3) U36_GGG(x1, x2, x3) = U36_GGG(x1, x2, x3) U37_GGG(x1, x2, x3) = U37_GGG(x1, x2, x3) U24_GGGG(x1, x2, x3, x4) = U24_GGGG(x1, x2, x3, x4) U21_GGG(x1, x2, x3) = U21_GGG(x1, x2, x3) U39_GG(x1, x2) = U39_GG(x1, x2) U40_GG(x1, x2) = U40_GG(x1, x2) U41_GG(x1, x2) = U41_GG(x1, x2) U42_GG(x1, x2) = U42_GG(x1, x2) U43_GG(x1, x2) = U43_GG(x1, x2) U44_GG(x1, x2) = U44_GG(x1, x2) U45_GG(x1, x2) = U45_GG(x1, x2) U46_GG(x1, x2) = U46_GG(x1, x2) U47_GG(x1, x2) = U47_GG(x1, x2) U48_GG(x1, x2) = U48_GG(x1, x2) U49_GG(x1, x2) = U49_GG(x1, x2) U50_GG(x1, x2) = U50_GG(x1, x2) U18_GGG(x1, x2, x3) = U18_GGG(x1, x2, x3) U52_GG(x1, x2) = U52_GG(x1, x2) U53_GG(x1, x2) = U53_GG(x1, x2) U54_GG(x1, x2) = U54_GG(x1, x2) U55_GG(x1, x2) = U55_GG(x1, x2) U56_GG(x1, x2) = U56_GG(x1, x2) U57_GG(x1, x2) = U57_GG(x1, x2) U58_GG(x1, x2) = U58_GG(x1, x2) U59_GG(x1, x2) = U59_GG(x1, x2) U60_GG(x1, x2) = U60_GG(x1, x2) U61_GG(x1, x2) = U61_GG(x1, x2) U62_GG(x1, x2) = U62_GG(x1, x2) U63_GG(x1, x2) = U63_GG(x1, x2) U15_GGG(x1, x2, x3) = U15_GGG(x1, x2, x3) U65_GG(x1, x2) = U65_GG(x1, x2) U66_GG(x1, x2) = U66_GG(x1, x2) U67_GG(x1, x2) = U67_GG(x1, x2) U68_GG(x1, x2) = U68_GG(x1, x2) U69_GG(x1, x2) = U69_GG(x1, x2) U70_GG(x1, x2) = U70_GG(x1, x2) U71_GG(x1, x2) = U71_GG(x1, x2) U72_GG(x1, x2) = U72_GG(x1, x2) U73_GG(x1, x2) = U73_GG(x1, x2) U74_GG(x1, x2) = U74_GG(x1, x2) U75_GG(x1, x2) = U75_GG(x1, x2) U76_GG(x1, x2) = U76_GG(x1, x2) U12_GGG(x1, x2, x3) = U12_GGG(x1, x2, x3) U78_GG(x1, x2) = U78_GG(x1, x2) U79_GG(x1, x2) = U79_GG(x1, x2) U80_GG(x1, x2) = U80_GG(x1, x2) U81_GG(x1, x2) = U81_GG(x1, x2) U82_GG(x1, x2) = U82_GG(x1, x2) U83_GG(x1, x2) = U83_GG(x1, x2) U84_GG(x1, x2) = U84_GG(x1, x2) U85_GG(x1, x2) = U85_GG(x1, x2) U86_GG(x1, x2) = U86_GG(x1, x2) U87_GG(x1, x2) = U87_GG(x1, x2) U88_GG(x1, x2) = U88_GG(x1, x2) U89_GG(x1, x2) = U89_GG(x1, x2) U9_GGG(x1, x2, x3) = U9_GGG(x1, x2, x3) U91_GG(x1, x2) = U91_GG(x1, x2) U92_GG(x1, x2) = U92_GG(x1, x2) U93_GG(x1, x2) = U93_GG(x1, x2) U94_GG(x1, x2) = U94_GG(x1, x2) U95_GG(x1, x2) = U95_GG(x1, x2) U96_GG(x1, x2) = U96_GG(x1, x2) U97_GG(x1, x2) = U97_GG(x1, x2) U98_GG(x1, x2) = U98_GG(x1, x2) U99_GG(x1, x2) = U99_GG(x1, x2) U100_GG(x1, x2) = U100_GG(x1, x2) U101_GG(x1, x2) = U101_GG(x1, x2) U102_GG(x1, x2) = U102_GG(x1, x2) U6_GGG(x1, x2, x3) = U6_GGG(x1, x2, x3) U104_GG(x1, x2) = U104_GG(x1, x2) U105_GG(x1, x2) = U105_GG(x1, x2) U106_GG(x1, x2) = U106_GG(x1, x2) U107_GG(x1, x2) = U107_GG(x1, x2) U108_GG(x1, x2) = U108_GG(x1, x2) U109_GG(x1, x2) = U109_GG(x1, x2) U110_GG(x1, x2) = U110_GG(x1, x2) U111_GG(x1, x2) = U111_GG(x1, x2) U112_GG(x1, x2) = U112_GG(x1, x2) U113_GG(x1, x2) = U113_GG(x1, x2) U114_GG(x1, x2) = U114_GG(x1, x2) U115_GG(x1, x2) = U115_GG(x1, x2) U3_AGG(x1, x2, x3) = U3_AGG(x1, x2, x3) U117_AG(x1, x2) = U117_AG(x1, x2) U118_AG(x1, x2) = U118_AG(x1, x2) U119_AG(x1, x2) = U119_AG(x1, x2) U120_AG(x1, x2) = U120_AG(x1, x2) U121_AG(x1, x2) = U121_AG(x1, x2) U122_AG(x1, x2) = U122_AG(x1, x2) U123_AG(x1, x2) = U123_AG(x1, x2) U124_AG(x1, x2) = U124_AG(x1, x2) U125_AG(x1, x2) = U125_AG(x1, x2) U126_AG(x1, x2) = U126_AG(x1, x2) U127_AG(x1, x2) = U127_AG(x1, x2) U128_AG(x1, x2) = U128_AG(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (109) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 245 less nodes. ---------------------------------------- (110) Complex Obligation (AND) ---------------------------------------- (111) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> LOG2O_IN_GGGG(X1, s(s(s(s(s(s(s(0))))))), X2, X3) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> LOG2O_IN_GGGG(X1, s(X2), X3, X4) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (112) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> LOG2O_IN_GGGG(X1, s(s(s(s(s(s(s(0))))))), X2, X3) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> LOG2O_IN_GGGG(X1, s(X2), X3, X4) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (114) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: LOG2N_IN_GGG(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X1)))))))))))))), X2, X3) -> LOG2O_IN_GGGG(X1, s(s(s(s(s(s(s(0))))))), X2, X3) LOG2O_IN_GGGG(s(s(X1)), X2, X3, X4) -> LOG2O_IN_GGGG(X1, s(X2), X3, X4) LOG2O_IN_GGGG(0, s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) LOG2O_IN_GGGG(s(0), s(X1), X2, X3) -> LOG2N_IN_GGG(X1, s(X2), X3) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(LOG2N_IN_GGG(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(LOG2O_IN_GGGG(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(s(x_1)) = 1 + x_1 ---------------------------------------- (115) Obligation: Q DP problem: P is empty. R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (116) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (117) YES ---------------------------------------- (118) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2M_IN_GGG(s(s(X1)), X2, X3) -> LOG2M_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (119) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (120) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2M_IN_GGG(s(s(X1)), X2, X3) -> LOG2M_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (121) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2M_IN_GGG(s(s(X1)), X2, X3) -> LOG2M_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (122) YES ---------------------------------------- (123) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2K_IN_GGG(s(s(X1)), X2, X3) -> LOG2K_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (124) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2K_IN_GGG(s(s(X1)), X2, X3) -> LOG2K_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (126) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2K_IN_GGG(s(s(X1)), X2, X3) -> LOG2K_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (127) YES ---------------------------------------- (128) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2I_IN_GGG(s(s(X1)), X2, X3) -> LOG2I_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (129) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (130) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2I_IN_GGG(s(s(X1)), X2, X3) -> LOG2I_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (131) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2I_IN_GGG(s(s(X1)), X2, X3) -> LOG2I_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (132) YES ---------------------------------------- (133) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2G_IN_GGG(s(s(X1)), X2, X3) -> LOG2G_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (134) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (135) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2G_IN_GGG(s(s(X1)), X2, X3) -> LOG2G_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (136) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2G_IN_GGG(s(s(X1)), X2, X3) -> LOG2G_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (137) YES ---------------------------------------- (138) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2E_IN_GGG(s(s(X1)), X2, X3) -> LOG2E_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (139) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (140) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2E_IN_GGG(s(s(X1)), X2, X3) -> LOG2E_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (141) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2E_IN_GGG(s(s(X1)), X2, X3) -> LOG2E_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (142) YES ---------------------------------------- (143) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2C_IN_GGG(s(s(X1)), X2, X3) -> LOG2C_IN_GGG(X1, s(X2), X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (144) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (145) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2C_IN_GGG(s(s(X1)), X2, X3) -> LOG2C_IN_GGG(X1, s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (146) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *LOG2C_IN_GGG(s(s(X1)), X2, X3) -> LOG2C_IN_GGG(X1, s(X2), X3) The graph contains the following edges 1 > 1, 3 >= 3 ---------------------------------------- (147) YES ---------------------------------------- (148) Obligation: Pi DP problem: The TRS P consists of the following rules: LOG2A_IN_AGG(s(s(X1)), X2, X3) -> LOG2A_IN_AGG(X1, s(X2), X3) R is empty. The argument filtering Pi contains the following mapping: s(x1) = s(x1) LOG2A_IN_AGG(x1, x2, x3) = LOG2A_IN_AGG(x2, x3) We have to consider all (P,R,Pi)-chains ---------------------------------------- (149) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (150) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2A_IN_AGG(X2, X3) -> LOG2A_IN_AGG(s(X2), X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (151) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2A_IN_AGG(X2, X3) -> LOG2A_IN_AGG(s(X2), X3) we obtained the following new rules [LPAR04]: (LOG2A_IN_AGG(s(z0), z1) -> LOG2A_IN_AGG(s(s(z0)), z1),LOG2A_IN_AGG(s(z0), z1) -> LOG2A_IN_AGG(s(s(z0)), z1)) ---------------------------------------- (152) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2A_IN_AGG(s(z0), z1) -> LOG2A_IN_AGG(s(s(z0)), z1) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (153) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule LOG2A_IN_AGG(s(z0), z1) -> LOG2A_IN_AGG(s(s(z0)), z1) we obtained the following new rules [LPAR04]: (LOG2A_IN_AGG(s(s(z0)), z1) -> LOG2A_IN_AGG(s(s(s(z0))), z1),LOG2A_IN_AGG(s(s(z0)), z1) -> LOG2A_IN_AGG(s(s(s(z0))), z1)) ---------------------------------------- (154) Obligation: Q DP problem: The TRS P consists of the following rules: LOG2A_IN_AGG(s(s(z0)), z1) -> LOG2A_IN_AGG(s(s(s(z0))), z1) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (155) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = LOG2A_IN_AGG(s(s(z0)), z1) evaluates to t =LOG2A_IN_AGG(s(s(s(z0))), z1) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [z0 / s(z0)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from LOG2A_IN_AGG(s(s(z0)), z1) to LOG2A_IN_AGG(s(s(s(z0))), z1). ---------------------------------------- (156) NO