10.29/4.04 MAYBE 10.68/4.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 10.68/4.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.68/4.08 10.68/4.08 10.68/4.08 Left Termination of the query pattern 10.68/4.08 10.68/4.08 log2(a,g) 10.68/4.08 10.68/4.08 w.r.t. the given Prolog program could not be shown: 10.68/4.08 10.68/4.08 (0) Prolog 10.68/4.08 (1) PrologToPiTRSProof [SOUND, 0 ms] 10.68/4.08 (2) PiTRS 10.68/4.08 (3) DependencyPairsProof [EQUIVALENT, 18 ms] 10.68/4.08 (4) PiDP 10.68/4.08 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (6) AND 10.68/4.08 (7) PiDP 10.68/4.08 (8) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (9) PiDP 10.68/4.08 (10) PiDPToQDPProof [SOUND, 13 ms] 10.68/4.08 (11) QDP 10.68/4.08 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.68/4.08 (13) YES 10.68/4.08 (14) PiDP 10.68/4.08 (15) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (16) PiDP 10.68/4.08 (17) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (18) QDP 10.68/4.08 (19) MRRProof [EQUIVALENT, 33 ms] 10.68/4.08 (20) QDP 10.68/4.08 (21) DependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (22) TRUE 10.68/4.08 (23) PiDP 10.68/4.08 (24) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (25) PiDP 10.68/4.08 (26) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (27) QDP 10.68/4.08 (28) PrologToPiTRSProof [SOUND, 0 ms] 10.68/4.08 (29) PiTRS 10.68/4.08 (30) DependencyPairsProof [EQUIVALENT, 1 ms] 10.68/4.08 (31) PiDP 10.68/4.08 (32) DependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (33) AND 10.68/4.08 (34) PiDP 10.68/4.08 (35) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (36) PiDP 10.68/4.08 (37) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (38) QDP 10.68/4.08 (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.68/4.08 (40) YES 10.68/4.08 (41) PiDP 10.68/4.08 (42) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (43) PiDP 10.68/4.08 (44) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (45) QDP 10.68/4.08 (46) TransformationProof [EQUIVALENT, 0 ms] 10.68/4.08 (47) QDP 10.68/4.08 (48) QDPOrderProof [EQUIVALENT, 29 ms] 10.68/4.08 (49) QDP 10.68/4.08 (50) QDPQMonotonicMRRProof [EQUIVALENT, 20 ms] 10.68/4.08 (51) QDP 10.68/4.08 (52) PiDP 10.68/4.08 (53) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (54) PiDP 10.68/4.08 (55) PrologToDTProblemTransformerProof [SOUND, 55 ms] 10.68/4.08 (56) TRIPLES 10.68/4.08 (57) TriplesToPiDPProof [SOUND, 22 ms] 10.68/4.08 (58) PiDP 10.68/4.08 (59) DependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (60) AND 10.68/4.08 (61) PiDP 10.68/4.08 (62) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (63) PiDP 10.68/4.08 (64) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (65) QDP 10.68/4.08 (66) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.68/4.08 (67) YES 10.68/4.08 (68) PiDP 10.68/4.08 (69) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (70) PiDP 10.68/4.08 (71) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (72) QDP 10.68/4.08 (73) TransformationProof [EQUIVALENT, 0 ms] 10.68/4.08 (74) QDP 10.68/4.08 (75) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (76) QDP 10.68/4.08 (77) QReductionProof [EQUIVALENT, 0 ms] 10.68/4.08 (78) QDP 10.68/4.08 (79) QDPOrderProof [EQUIVALENT, 9 ms] 10.68/4.08 (80) QDP 10.68/4.08 (81) PisEmptyProof [EQUIVALENT, 0 ms] 10.68/4.08 (82) YES 10.68/4.08 (83) PiDP 10.68/4.08 (84) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (85) PiDP 10.68/4.08 (86) PiDPToQDPProof [SOUND, 0 ms] 10.68/4.08 (87) QDP 10.68/4.08 (88) PrologToTRSTransformerProof [SOUND, 68 ms] 10.68/4.08 (89) QTRS 10.68/4.08 (90) DependencyPairsProof [EQUIVALENT, 0 ms] 10.68/4.08 (91) QDP 10.68/4.08 (92) DependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (93) AND 10.68/4.08 (94) QDP 10.68/4.08 (95) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (96) QDP 10.68/4.08 (97) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.68/4.08 (98) YES 10.68/4.08 (99) QDP 10.68/4.08 (100) QDP 10.68/4.08 (101) UsableRulesProof [EQUIVALENT, 0 ms] 10.68/4.08 (102) QDP 10.68/4.08 (103) PrologToIRSwTTransformerProof [SOUND, 53 ms] 10.68/4.08 (104) AND 10.68/4.08 (105) IRSwT 10.68/4.08 (106) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (107) TRUE 10.68/4.08 (108) IRSwT 10.68/4.08 (109) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (110) TRUE 10.68/4.08 (111) IRSwT 10.68/4.08 (112) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 10.68/4.08 (113) IRSwT 10.68/4.08 (114) IntTRSCompressionProof [EQUIVALENT, 20 ms] 10.68/4.08 (115) IRSwT 10.68/4.08 (116) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 10.68/4.08 (117) IRSwT 10.68/4.08 (118) IRSwTTerminationDigraphProof [EQUIVALENT, 6 ms] 10.68/4.08 (119) IRSwT 10.68/4.08 (120) FilterProof [EQUIVALENT, 0 ms] 10.68/4.08 (121) IntTRS 10.68/4.08 (122) IntTRSPeriodicNontermProof [COMPLETE, 4 ms] 10.68/4.08 (123) NO 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (0) 10.68/4.08 Obligation: 10.68/4.08 Clauses: 10.68/4.08 10.68/4.08 log2(X, Y) :- log2(X, 0, Y). 10.68/4.08 log2(0, I, I). 10.68/4.08 log2(s(0), I, I). 10.68/4.08 log2(s(s(X)), I, Y) :- ','(half(s(s(X)), X1), log2(X1, s(I), Y)). 10.68/4.08 half(0, 0). 10.68/4.08 half(s(0), 0). 10.68/4.08 half(s(s(X)), s(Y)) :- half(X, Y). 10.68/4.08 10.68/4.08 10.68/4.08 Query: log2(a,g) 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (1) PrologToPiTRSProof (SOUND) 10.68/4.08 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 10.68/4.08 10.68/4.08 log2_in_2: (f,b) 10.68/4.08 10.68/4.08 log2_in_3: (f,b,b) (b,b,b) 10.68/4.08 10.68/4.08 half_in_2: (f,f) (b,f) 10.68/4.08 10.68/4.08 Transforming Prolog into the following Term Rewriting System: 10.68/4.08 10.68/4.08 Pi-finite rewrite system: 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (2) 10.68/4.08 Obligation: 10.68/4.08 Pi-finite rewrite system: 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (3) DependencyPairsProof (EQUIVALENT) 10.68/4.08 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 LOG2_IN_AG(X, Y) -> LOG2_IN_AGG(X, 0, Y) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> U2_AGG(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> HALF_IN_AA(s(s(X)), X1) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> U4_AA(X, Y, half_in_aa(X, Y)) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_AGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> HALF_IN_GA(s(s(X)), X1) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> U4_GA(X, Y, half_in_ga(X, Y)) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_GGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) 10.68/4.08 10.68/4.08 U1_AG(x1, x2, x3) = U1_AG(x3) 10.68/4.08 10.68/4.08 LOG2_IN_AGG(x1, x2, x3) = LOG2_IN_AGG(x2, x3) 10.68/4.08 10.68/4.08 U2_AGG(x1, x2, x3, x4) = U2_AGG(x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.08 10.68/4.08 U4_AA(x1, x2, x3) = U4_AA(x3) 10.68/4.08 10.68/4.08 U3_AGG(x1, x2, x3, x4) = U3_AGG(x1, x4) 10.68/4.08 10.68/4.08 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_GGG(x1, x2, x3, x4) = U2_GGG(x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.08 10.68/4.08 U4_GA(x1, x2, x3) = U4_GA(x3) 10.68/4.08 10.68/4.08 U3_GGG(x1, x2, x3, x4) = U3_GGG(x4) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (4) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 LOG2_IN_AG(X, Y) -> LOG2_IN_AGG(X, 0, Y) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> U2_AGG(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> HALF_IN_AA(s(s(X)), X1) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> U4_AA(X, Y, half_in_aa(X, Y)) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_AGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> HALF_IN_GA(s(s(X)), X1) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> U4_GA(X, Y, half_in_ga(X, Y)) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_GGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) 10.68/4.08 10.68/4.08 U1_AG(x1, x2, x3) = U1_AG(x3) 10.68/4.08 10.68/4.08 LOG2_IN_AGG(x1, x2, x3) = LOG2_IN_AGG(x2, x3) 10.68/4.08 10.68/4.08 U2_AGG(x1, x2, x3, x4) = U2_AGG(x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.08 10.68/4.08 U4_AA(x1, x2, x3) = U4_AA(x3) 10.68/4.08 10.68/4.08 U3_AGG(x1, x2, x3, x4) = U3_AGG(x1, x4) 10.68/4.08 10.68/4.08 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_GGG(x1, x2, x3, x4) = U2_GGG(x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.08 10.68/4.08 U4_GA(x1, x2, x3) = U4_GA(x3) 10.68/4.08 10.68/4.08 U3_GGG(x1, x2, x3, x4) = U3_GGG(x4) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (5) DependencyGraphProof (EQUIVALENT) 10.68/4.08 The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 10 less nodes. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (6) 10.68/4.08 Complex Obligation (AND) 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (7) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (8) UsableRulesProof (EQUIVALENT) 10.68/4.08 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (9) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 10.68/4.08 R is empty. 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (10) PiDPToQDPProof (SOUND) 10.68/4.08 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (11) 10.68/4.08 Obligation: 10.68/4.08 Q DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_GA(s(s(X))) -> HALF_IN_GA(X) 10.68/4.08 10.68/4.08 R is empty. 10.68/4.08 Q is empty. 10.68/4.08 We have to consider all (P,Q,R)-chains. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (12) QDPSizeChangeProof (EQUIVALENT) 10.68/4.08 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. 10.68/4.08 10.68/4.08 From the DPs we obtained the following set of size-change graphs: 10.68/4.08 *HALF_IN_GA(s(s(X))) -> HALF_IN_GA(X) 10.68/4.08 The graph contains the following edges 1 > 1 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (13) 10.68/4.08 YES 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (14) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_GGG(x1, x2, x3, x4) = U2_GGG(x2, x3, x4) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (15) UsableRulesProof (EQUIVALENT) 10.68/4.08 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (16) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_GGG(x1, x2, x3, x4) = U2_GGG(x2, x3, x4) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (17) PiDPToQDPProof (SOUND) 10.68/4.08 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (18) 10.68/4.08 Obligation: 10.68/4.08 Q DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 U2_GGG(I, Y, half_out_ga(X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(I, Y, half_in_ga(s(s(X)))) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 half_in_ga(s(s(X))) -> U4_ga(half_in_ga(X)) 10.68/4.08 U4_ga(half_out_ga(Y)) -> half_out_ga(s(Y)) 10.68/4.08 half_in_ga(0) -> half_out_ga(0) 10.68/4.08 half_in_ga(s(0)) -> half_out_ga(0) 10.68/4.08 10.68/4.08 The set Q consists of the following terms: 10.68/4.08 10.68/4.08 half_in_ga(x0) 10.68/4.08 U4_ga(x0) 10.68/4.08 10.68/4.08 We have to consider all (P,Q,R)-chains. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (19) MRRProof (EQUIVALENT) 10.68/4.08 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. 10.68/4.08 10.68/4.08 Strictly oriented dependency pairs: 10.68/4.08 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(I, Y, half_in_ga(s(s(X)))) 10.68/4.08 10.68/4.08 Strictly oriented rules of the TRS R: 10.68/4.08 10.68/4.08 half_in_ga(s(0)) -> half_out_ga(0) 10.68/4.08 10.68/4.08 Used ordering: Polynomial interpretation [POLO]: 10.68/4.08 10.68/4.08 POL(0) = 0 10.68/4.08 POL(LOG2_IN_GGG(x_1, x_2, x_3)) = 2*x_1 + x_2 + x_3 10.68/4.08 POL(U2_GGG(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 10.68/4.08 POL(U4_ga(x_1)) = 2 + x_1 10.68/4.08 POL(half_in_ga(x_1)) = x_1 10.68/4.08 POL(half_out_ga(x_1)) = 2*x_1 10.68/4.08 POL(s(x_1)) = 1 + x_1 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (20) 10.68/4.08 Obligation: 10.68/4.08 Q DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 U2_GGG(I, Y, half_out_ga(X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 half_in_ga(s(s(X))) -> U4_ga(half_in_ga(X)) 10.68/4.08 U4_ga(half_out_ga(Y)) -> half_out_ga(s(Y)) 10.68/4.08 half_in_ga(0) -> half_out_ga(0) 10.68/4.08 10.68/4.08 The set Q consists of the following terms: 10.68/4.08 10.68/4.08 half_in_ga(x0) 10.68/4.08 U4_ga(x0) 10.68/4.08 10.68/4.08 We have to consider all (P,Q,R)-chains. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (21) DependencyGraphProof (EQUIVALENT) 10.68/4.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (22) 10.68/4.08 TRUE 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (23) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1) 10.68/4.08 10.68/4.08 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (24) UsableRulesProof (EQUIVALENT) 10.68/4.08 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (25) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 10.68/4.08 R is empty. 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (26) PiDPToQDPProof (SOUND) 10.68/4.08 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (27) 10.68/4.08 Obligation: 10.68/4.08 Q DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 HALF_IN_AA -> HALF_IN_AA 10.68/4.08 10.68/4.08 R is empty. 10.68/4.08 Q is empty. 10.68/4.08 We have to consider all (P,Q,R)-chains. 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (28) PrologToPiTRSProof (SOUND) 10.68/4.08 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 10.68/4.08 10.68/4.08 log2_in_2: (f,b) 10.68/4.08 10.68/4.08 log2_in_3: (f,b,b) (b,b,b) 10.68/4.08 10.68/4.08 half_in_2: (f,f) (b,f) 10.68/4.08 10.68/4.08 Transforming Prolog into the following Term Rewriting System: 10.68/4.08 10.68/4.08 Pi-finite rewrite system: 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (29) 10.68/4.08 Obligation: 10.68/4.08 Pi-finite rewrite system: 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.08 10.68/4.08 10.68/4.08 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (30) DependencyPairsProof (EQUIVALENT) 10.68/4.08 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 LOG2_IN_AG(X, Y) -> LOG2_IN_AGG(X, 0, Y) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> U2_AGG(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> HALF_IN_AA(s(s(X)), X1) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> U4_AA(X, Y, half_in_aa(X, Y)) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_AGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> HALF_IN_GA(s(s(X)), X1) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> U4_GA(X, Y, half_in_ga(X, Y)) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_GGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 0 = 0 10.68/4.08 10.68/4.08 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.08 10.68/4.08 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.08 10.68/4.08 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.08 10.68/4.08 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.08 10.68/4.08 LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) 10.68/4.08 10.68/4.08 U1_AG(x1, x2, x3) = U1_AG(x2, x3) 10.68/4.08 10.68/4.08 LOG2_IN_AGG(x1, x2, x3) = LOG2_IN_AGG(x2, x3) 10.68/4.08 10.68/4.08 U2_AGG(x1, x2, x3, x4) = U2_AGG(x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.08 10.68/4.08 U4_AA(x1, x2, x3) = U4_AA(x3) 10.68/4.08 10.68/4.08 U3_AGG(x1, x2, x3, x4) = U3_AGG(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_GGG(x1, x2, x3, x4) = U2_GGG(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.08 10.68/4.08 U4_GA(x1, x2, x3) = U4_GA(x1, x3) 10.68/4.08 10.68/4.08 U3_GGG(x1, x2, x3, x4) = U3_GGG(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 10.68/4.08 We have to consider all (P,R,Pi)-chains 10.68/4.08 ---------------------------------------- 10.68/4.08 10.68/4.08 (31) 10.68/4.08 Obligation: 10.68/4.08 Pi DP problem: 10.68/4.08 The TRS P consists of the following rules: 10.68/4.08 10.68/4.08 LOG2_IN_AG(X, Y) -> U1_AG(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 LOG2_IN_AG(X, Y) -> LOG2_IN_AGG(X, 0, Y) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> U2_AGG(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 LOG2_IN_AGG(s(s(X)), I, Y) -> HALF_IN_AA(s(s(X)), X1) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> U4_AA(X, Y, half_in_aa(X, Y)) 10.68/4.08 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_AGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_AGG(X, I, Y, half_out_aa(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 LOG2_IN_GGG(s(s(X)), I, Y) -> HALF_IN_GA(s(s(X)), X1) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> U4_GA(X, Y, half_in_ga(X, Y)) 10.68/4.08 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_GGG(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.08 10.68/4.08 The TRS R consists of the following rules: 10.68/4.08 10.68/4.08 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.08 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.08 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.08 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.08 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.08 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.08 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.08 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.08 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.08 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.08 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.08 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.08 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.08 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.08 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.08 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.08 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.08 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.08 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.08 10.68/4.08 The argument filtering Pi contains the following mapping: 10.68/4.08 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.08 10.68/4.08 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.08 10.68/4.08 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.08 10.68/4.08 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.08 10.68/4.08 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.08 10.68/4.08 half_in_aa(x1, x2) = half_in_aa 10.68/4.08 10.68/4.08 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.08 10.68/4.08 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.08 10.68/4.08 s(x1) = s(x1) 10.68/4.08 10.68/4.08 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.08 10.68/4.08 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 0 = 0 10.68/4.12 10.68/4.12 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.12 10.68/4.12 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.12 10.68/4.12 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.12 10.68/4.12 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.12 10.68/4.12 LOG2_IN_AG(x1, x2) = LOG2_IN_AG(x2) 10.68/4.12 10.68/4.12 U1_AG(x1, x2, x3) = U1_AG(x2, x3) 10.68/4.12 10.68/4.12 LOG2_IN_AGG(x1, x2, x3) = LOG2_IN_AGG(x2, x3) 10.68/4.12 10.68/4.12 U2_AGG(x1, x2, x3, x4) = U2_AGG(x2, x3, x4) 10.68/4.12 10.68/4.12 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.12 10.68/4.12 U4_AA(x1, x2, x3) = U4_AA(x3) 10.68/4.12 10.68/4.12 U3_AGG(x1, x2, x3, x4) = U3_AGG(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_GGG(x1, x2, x3, x4) = U2_GGG(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.12 10.68/4.12 U4_GA(x1, x2, x3) = U4_GA(x1, x3) 10.68/4.12 10.68/4.12 U3_GGG(x1, x2, x3, x4) = U3_GGG(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (32) DependencyGraphProof (EQUIVALENT) 10.68/4.12 The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 10 less nodes. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (33) 10.68/4.12 Complex Obligation (AND) 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (34) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.12 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.12 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.12 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.12 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.12 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.12 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.12 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.12 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.12 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.12 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.12 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.12 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.12 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.12 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.12 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.12 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.12 10.68/4.12 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.12 10.68/4.12 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.12 10.68/4.12 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_aa(x1, x2) = half_in_aa 10.68/4.12 10.68/4.12 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.12 10.68/4.12 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.12 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 0 = 0 10.68/4.12 10.68/4.12 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.12 10.68/4.12 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.12 10.68/4.12 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.12 10.68/4.12 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.12 10.68/4.12 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (35) UsableRulesProof (EQUIVALENT) 10.68/4.12 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (36) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 HALF_IN_GA(s(s(X)), s(Y)) -> HALF_IN_GA(X, Y) 10.68/4.12 10.68/4.12 R is empty. 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 HALF_IN_GA(x1, x2) = HALF_IN_GA(x1) 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (37) PiDPToQDPProof (SOUND) 10.68/4.12 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (38) 10.68/4.12 Obligation: 10.68/4.12 Q DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 HALF_IN_GA(s(s(X))) -> HALF_IN_GA(X) 10.68/4.12 10.68/4.12 R is empty. 10.68/4.12 Q is empty. 10.68/4.12 We have to consider all (P,Q,R)-chains. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (39) QDPSizeChangeProof (EQUIVALENT) 10.68/4.12 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. 10.68/4.12 10.68/4.12 From the DPs we obtained the following set of size-change graphs: 10.68/4.12 *HALF_IN_GA(s(s(X))) -> HALF_IN_GA(X) 10.68/4.12 The graph contains the following edges 1 > 1 10.68/4.12 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (40) 10.68/4.12 YES 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (41) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.12 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.12 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.12 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.12 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.12 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.12 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.12 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.12 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.12 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.12 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.12 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.12 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.12 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.12 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.12 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.12 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.12 10.68/4.12 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.12 10.68/4.12 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.12 10.68/4.12 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_aa(x1, x2) = half_in_aa 10.68/4.12 10.68/4.12 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.12 10.68/4.12 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.12 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 0 = 0 10.68/4.12 10.68/4.12 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.12 10.68/4.12 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.12 10.68/4.12 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.12 10.68/4.12 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.12 10.68/4.12 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_GGG(x1, x2, x3, x4) = U2_GGG(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (42) UsableRulesProof (EQUIVALENT) 10.68/4.12 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (43) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.12 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.12 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 0 = 0 10.68/4.12 10.68/4.12 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.12 10.68/4.12 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.12 10.68/4.12 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.12 10.68/4.12 LOG2_IN_GGG(x1, x2, x3) = LOG2_IN_GGG(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_GGG(x1, x2, x3, x4) = U2_GGG(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (44) PiDPToQDPProof (SOUND) 10.68/4.12 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (45) 10.68/4.12 Obligation: 10.68/4.12 Q DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)))) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X))) -> U4_ga(X, half_in_ga(X)) 10.68/4.12 U4_ga(X, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 half_in_ga(0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0)) -> half_out_ga(s(0), 0) 10.68/4.12 10.68/4.12 The set Q consists of the following terms: 10.68/4.12 10.68/4.12 half_in_ga(x0) 10.68/4.12 U4_ga(x0, x1) 10.68/4.12 10.68/4.12 We have to consider all (P,Q,R)-chains. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (46) TransformationProof (EQUIVALENT) 10.68/4.12 By rewriting [LPAR04] the rule LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, half_in_ga(s(s(X)))) at position [3] we obtained the following new rules [LPAR04]: 10.68/4.12 10.68/4.12 (LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, U4_ga(X, half_in_ga(X))),LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, U4_ga(X, half_in_ga(X)))) 10.68/4.12 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (47) 10.68/4.12 Obligation: 10.68/4.12 Q DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, U4_ga(X, half_in_ga(X))) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X))) -> U4_ga(X, half_in_ga(X)) 10.68/4.12 U4_ga(X, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 half_in_ga(0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0)) -> half_out_ga(s(0), 0) 10.68/4.12 10.68/4.12 The set Q consists of the following terms: 10.68/4.12 10.68/4.12 half_in_ga(x0) 10.68/4.12 U4_ga(x0, x1) 10.68/4.12 10.68/4.12 We have to consider all (P,Q,R)-chains. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (48) QDPOrderProof (EQUIVALENT) 10.68/4.12 We use the reduction pair processor [LPAR04,JAR06]. 10.68/4.12 10.68/4.12 10.68/4.12 The following pairs can be oriented strictly and are deleted. 10.68/4.12 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, U4_ga(X, half_in_ga(X))) 10.68/4.12 The remaining pairs can at least be oriented weakly. 10.68/4.12 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 10.68/4.12 10.68/4.12 POL( U2_GGG_4(x_1, ..., x_4) ) = 2x_4 10.68/4.12 POL( U4_ga_2(x_1, x_2) ) = 2x_2 10.68/4.12 POL( half_in_ga_1(x_1) ) = 2x_1 10.68/4.12 POL( s_1(x_1) ) = 2x_1 + 1 10.68/4.12 POL( 0 ) = 1 10.68/4.12 POL( half_out_ga_2(x_1, x_2) ) = x_2 + 1 10.68/4.12 POL( LOG2_IN_GGG_3(x_1, ..., x_3) ) = 2x_1 + 2 10.68/4.12 10.68/4.12 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X))) -> U4_ga(X, half_in_ga(X)) 10.68/4.12 half_in_ga(0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0)) -> half_out_ga(s(0), 0) 10.68/4.12 U4_ga(X, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (49) 10.68/4.12 Obligation: 10.68/4.12 Q DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X))) -> U4_ga(X, half_in_ga(X)) 10.68/4.12 U4_ga(X, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 half_in_ga(0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0)) -> half_out_ga(s(0), 0) 10.68/4.12 10.68/4.12 The set Q consists of the following terms: 10.68/4.12 10.68/4.12 half_in_ga(x0) 10.68/4.12 U4_ga(x0, x1) 10.68/4.12 10.68/4.12 We have to consider all (P,Q,R)-chains. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (50) QDPQMonotonicMRRProof (EQUIVALENT) 10.68/4.12 By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain. 10.68/4.12 10.68/4.12 10.68/4.12 Strictly oriented rules of the TRS R: 10.68/4.12 10.68/4.12 half_in_ga(s(0)) -> half_out_ga(s(0), 0) 10.68/4.12 10.68/4.12 Used ordering: Polynomial interpretation [POLO]: 10.68/4.12 10.68/4.12 POL(0) = 2 10.68/4.12 POL(LOG2_IN_GGG(x_1, x_2, x_3)) = 2*x_1 + 2*x_3 10.68/4.12 POL(U2_GGG(x_1, x_2, x_3, x_4)) = 2*x_3 + 2*x_4 10.68/4.12 POL(U4_ga(x_1, x_2)) = 2*x_2 10.68/4.12 POL(half_in_ga(x_1)) = 2*x_1 10.68/4.12 POL(half_out_ga(x_1, x_2)) = 2*x_2 10.68/4.12 POL(s(x_1)) = 2*x_1 10.68/4.12 10.68/4.12 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (51) 10.68/4.12 Obligation: 10.68/4.12 Q DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 U2_GGG(X, I, Y, half_out_ga(s(s(X)), X1)) -> LOG2_IN_GGG(X1, s(I), Y) 10.68/4.12 LOG2_IN_GGG(s(s(X)), I, Y) -> U2_GGG(X, I, Y, U4_ga(X, half_in_ga(X))) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 half_in_ga(s(s(X))) -> U4_ga(X, half_in_ga(X)) 10.68/4.12 U4_ga(X, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 half_in_ga(0) -> half_out_ga(0, 0) 10.68/4.12 10.68/4.12 The set Q consists of the following terms: 10.68/4.12 10.68/4.12 half_in_ga(x0) 10.68/4.12 U4_ga(x0, x1) 10.68/4.12 10.68/4.12 We have to consider all (P,Q,R)-chains. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (52) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.12 10.68/4.12 The TRS R consists of the following rules: 10.68/4.12 10.68/4.12 log2_in_ag(X, Y) -> U1_ag(X, Y, log2_in_agg(X, 0, Y)) 10.68/4.12 log2_in_agg(0, I, I) -> log2_out_agg(0, I, I) 10.68/4.12 log2_in_agg(s(0), I, I) -> log2_out_agg(s(0), I, I) 10.68/4.12 log2_in_agg(s(s(X)), I, Y) -> U2_agg(X, I, Y, half_in_aa(s(s(X)), X1)) 10.68/4.12 half_in_aa(0, 0) -> half_out_aa(0, 0) 10.68/4.12 half_in_aa(s(0), 0) -> half_out_aa(s(0), 0) 10.68/4.12 half_in_aa(s(s(X)), s(Y)) -> U4_aa(X, Y, half_in_aa(X, Y)) 10.68/4.12 U4_aa(X, Y, half_out_aa(X, Y)) -> half_out_aa(s(s(X)), s(Y)) 10.68/4.12 U2_agg(X, I, Y, half_out_aa(s(s(X)), X1)) -> U3_agg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 log2_in_ggg(0, I, I) -> log2_out_ggg(0, I, I) 10.68/4.12 log2_in_ggg(s(0), I, I) -> log2_out_ggg(s(0), I, I) 10.68/4.12 log2_in_ggg(s(s(X)), I, Y) -> U2_ggg(X, I, Y, half_in_ga(s(s(X)), X1)) 10.68/4.12 half_in_ga(0, 0) -> half_out_ga(0, 0) 10.68/4.12 half_in_ga(s(0), 0) -> half_out_ga(s(0), 0) 10.68/4.12 half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y)) 10.68/4.12 U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y)) 10.68/4.12 U2_ggg(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_ggg(X, I, Y, log2_in_ggg(X1, s(I), Y)) 10.68/4.12 U3_ggg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_ggg(s(s(X)), I, Y) 10.68/4.12 U3_agg(X, I, Y, log2_out_ggg(X1, s(I), Y)) -> log2_out_agg(s(s(X)), I, Y) 10.68/4.12 U1_ag(X, Y, log2_out_agg(X, 0, Y)) -> log2_out_ag(X, Y) 10.68/4.12 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 log2_in_ag(x1, x2) = log2_in_ag(x2) 10.68/4.12 10.68/4.12 U1_ag(x1, x2, x3) = U1_ag(x2, x3) 10.68/4.12 10.68/4.12 log2_in_agg(x1, x2, x3) = log2_in_agg(x2, x3) 10.68/4.12 10.68/4.12 log2_out_agg(x1, x2, x3) = log2_out_agg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_agg(x1, x2, x3, x4) = U2_agg(x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_aa(x1, x2) = half_in_aa 10.68/4.12 10.68/4.12 half_out_aa(x1, x2) = half_out_aa(x1, x2) 10.68/4.12 10.68/4.12 U4_aa(x1, x2, x3) = U4_aa(x3) 10.68/4.12 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 U3_agg(x1, x2, x3, x4) = U3_agg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_in_ggg(x1, x2, x3) = log2_in_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 0 = 0 10.68/4.12 10.68/4.12 log2_out_ggg(x1, x2, x3) = log2_out_ggg(x1, x2, x3) 10.68/4.12 10.68/4.12 U2_ggg(x1, x2, x3, x4) = U2_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 half_in_ga(x1, x2) = half_in_ga(x1) 10.68/4.12 10.68/4.12 half_out_ga(x1, x2) = half_out_ga(x1, x2) 10.68/4.12 10.68/4.12 U4_ga(x1, x2, x3) = U4_ga(x1, x3) 10.68/4.12 10.68/4.12 U3_ggg(x1, x2, x3, x4) = U3_ggg(x1, x2, x3, x4) 10.68/4.12 10.68/4.12 log2_out_ag(x1, x2) = log2_out_ag(x1, x2) 10.68/4.12 10.68/4.12 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (53) UsableRulesProof (EQUIVALENT) 10.68/4.12 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (54) 10.68/4.12 Obligation: 10.68/4.12 Pi DP problem: 10.68/4.12 The TRS P consists of the following rules: 10.68/4.12 10.68/4.12 HALF_IN_AA(s(s(X)), s(Y)) -> HALF_IN_AA(X, Y) 10.68/4.12 10.68/4.12 R is empty. 10.68/4.12 The argument filtering Pi contains the following mapping: 10.68/4.12 s(x1) = s(x1) 10.68/4.12 10.68/4.12 HALF_IN_AA(x1, x2) = HALF_IN_AA 10.68/4.12 10.68/4.12 10.68/4.12 We have to consider all (P,R,Pi)-chains 10.68/4.12 ---------------------------------------- 10.68/4.12 10.68/4.12 (55) PrologToDTProblemTransformerProof (SOUND) 10.68/4.12 Built DT problem from termination graph DT10. 10.68/4.12 10.68/4.12 { 10.68/4.12 "root": 2, 10.68/4.12 "program": { 10.68/4.12 "directives": [], 10.68/4.12 "clauses": [ 10.68/4.12 [ 10.68/4.12 "(log2 X Y)", 10.68/4.12 "(log2 X (0) Y)" 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(log2 (0) I I)", 10.68/4.12 null 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(log2 (s (0)) I I)", 10.68/4.12 null 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(log2 (s (s X)) I Y)", 10.68/4.12 "(',' (half (s (s X)) X1) (log2 X1 (s I) Y))" 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(half (0) (0))", 10.68/4.12 null 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(half (s (0)) (0))", 10.68/4.12 null 10.68/4.12 ], 10.68/4.12 [ 10.68/4.12 "(half (s (s X)) (s Y))", 10.68/4.12 "(half X Y)" 10.68/4.12 ] 10.68/4.12 ] 10.68/4.12 }, 10.68/4.12 "graph": { 10.68/4.12 "nodes": { 10.68/4.12 "89": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T6"], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "type": "Nodes", 10.68/4.12 "350": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(half (s (s T36)) X90)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T36"], 10.68/4.12 "free": ["X90"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "351": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "352": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "353": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "354": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "355": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(true)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "356": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "357": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "478": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(',' (half (s (s T93)) X228) (log2 X228 (s (s T94)) T95))" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T93", 10.68/4.12 "T94", 10.68/4.12 "T95" 10.68/4.12 ], 10.68/4.12 "free": ["X228"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "358": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "479": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "90": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T6"], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "359": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 7, 10.68/4.12 "term": "(log2 T38 (s (s (s (0)))) T37)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T37", 10.68/4.12 "T38" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "91": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 2, 10.68/4.12 "term": "(log2 T7 (0) T6)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T6"], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "93": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(true)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "94": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "96": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "19": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 0, 10.68/4.12 "scope": 1, 10.68/4.12 "term": "(log2 T1 T2)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T2"], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "360": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(true)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "361": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "362": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "363": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(',' (half (s (s T43)) X113) (log2 X113 (s (s (s (s (0))))) T44))" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T43", 10.68/4.12 "T44" 10.68/4.12 ], 10.68/4.12 "free": ["X113"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "364": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "2": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(log2 T1 T2)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T2"], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "365": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(half (s (s T43)) X113)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T43"], 10.68/4.12 "free": ["X113"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "366": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "367": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "368": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "369": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 } 10.68/4.12 ], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "403": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(',' (half (s (s T57)) X159) (log2 X159 (s (s (s (s (s (s (0))))))) T58))" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T57", 10.68/4.12 "T58" 10.68/4.12 ], 10.68/4.12 "free": ["X159"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "404": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "406": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(half (s (s T57)) X159)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": ["T57"], 10.68/4.12 "free": ["X159"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "407": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T58", 10.68/4.12 "T59" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "370": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(true)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "371": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "372": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "373": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "374": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": 3, 10.68/4.12 "scope": 8, 10.68/4.12 "term": "(log2 T45 (s (s (s (s (0))))) T44)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T44", 10.68/4.12 "T45" 10.68/4.12 ], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "375": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(true)" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "376": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "377": { 10.68/4.12 "goal": [], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [], 10.68/4.12 "free": [], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "378": { 10.68/4.12 "goal": [{ 10.68/4.12 "clause": -1, 10.68/4.12 "scope": -1, 10.68/4.12 "term": "(',' (half (s (s T50)) X136) (log2 X136 (s (s (s (s (s (0)))))) T51))" 10.68/4.12 }], 10.68/4.12 "kb": { 10.68/4.12 "nonunifying": [], 10.68/4.12 "intvars": {}, 10.68/4.12 "arithmetic": { 10.68/4.12 "type": "PlainIntegerRelationState", 10.68/4.12 "relations": [] 10.68/4.12 }, 10.68/4.12 "ground": [ 10.68/4.12 "T50", 10.68/4.12 "T51" 10.68/4.12 ], 10.68/4.12 "free": ["X136"], 10.68/4.12 "exprvars": [] 10.68/4.12 } 10.68/4.12 }, 10.68/4.12 "411": { 10.68/4.12 "goal": [ 10.68/4.12 { 10.68/4.12 "clause": 1, 10.68/4.12 "scope": 10, 10.68/4.12 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.12 }, 10.68/4.12 { 10.68/4.12 "clause": 2, 10.68/4.12 "scope": 10, 10.68/4.12 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T58", 10.68/4.13 "T59" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "379": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "412": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T58", 10.68/4.13 "T59" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "413": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T58", 10.68/4.13 "T59" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "414": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "415": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "416": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "417": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T58", 10.68/4.13 "T59" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "418": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 10, 10.68/4.13 "term": "(log2 T59 (s (s (s (s (s (s (0))))))) T58)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T58", 10.68/4.13 "T59" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "419": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "380": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(half (s (s T50)) X136)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": ["T50"], 10.68/4.13 "free": ["X136"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "381": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "382": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "383": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "384": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "385": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "386": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "387": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "420": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "421": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "147": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 2, 10.68/4.13 "term": "(log2 T7 (0) T6)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": ["T6"], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "301": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "422": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(',' (half (s (s T64)) X182) (log2 X182 (s (s (s (s (s (s (s (0)))))))) T65))" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T64", 10.68/4.13 "T65" 10.68/4.13 ], 10.68/4.13 "free": ["X182"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "148": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 2, 10.68/4.13 "term": "(log2 T7 (0) T6)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": ["T6"], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "302": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "423": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "303": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "424": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(half (s (s T64)) X182)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": ["T64"], 10.68/4.13 "free": ["X182"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "425": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T65", 10.68/4.13 "T66" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "307": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 5, 10.68/4.13 "scope": 4, 10.68/4.13 "term": "(half T20 X35)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X35"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "308": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 6, 10.68/4.13 "scope": 4, 10.68/4.13 "term": "(half T20 X35)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X35"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "390": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "391": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 9, 10.68/4.13 "term": "(log2 T52 (s (s (s (s (s (0)))))) T51)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T51", 10.68/4.13 "T52" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "395": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "396": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "397": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "311": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "312": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "314": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "317": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(half T24 X44)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X44"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "318": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "283": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(',' (half (s (s T14)) X26) (log2 X26 (s (0)) T13))" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": ["T13"], 10.68/4.13 "free": ["X26"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "284": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "285": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X26"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "286": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T13", 10.68/4.13 "T15" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "440": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T65", 10.68/4.13 "T66" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "166": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "287": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 4, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 5, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 6, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X26"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "441": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T65", 10.68/4.13 "T66" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "288": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 5, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 6, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X26"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "321": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T13", 10.68/4.13 "T15" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "442": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 11, 10.68/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T65", 10.68/4.13 "T66" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "168": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "289": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 6, 10.68/4.13 "scope": 3, 10.68/4.13 "term": "(half (s (s T14)) X26)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": ["X26"], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "322": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": 1, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T13", 10.68/4.13 "T15" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "443": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "444": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "324": { 10.68/4.13 "goal": [ 10.68/4.13 { 10.68/4.13 "clause": 2, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 }, 10.68/4.13 { 10.68/4.13 "clause": 3, 10.68/4.13 "scope": 5, 10.68/4.13 "term": "(log2 T15 (s (0)) T13)" 10.68/4.13 } 10.68/4.13 ], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [ 10.68/4.13 "T13", 10.68/4.13 "T15" 10.68/4.13 ], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "445": { 10.68/4.13 "goal": [], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.68/4.13 }, 10.68/4.13 "ground": [], 10.68/4.13 "free": [], 10.68/4.13 "exprvars": [] 10.68/4.13 } 10.68/4.13 }, 10.68/4.13 "325": { 10.68/4.13 "goal": [{ 10.68/4.13 "clause": -1, 10.68/4.13 "scope": -1, 10.68/4.13 "term": "(true)" 10.68/4.13 }], 10.68/4.13 "kb": { 10.68/4.13 "nonunifying": [], 10.68/4.13 "intvars": {}, 10.68/4.13 "arithmetic": { 10.68/4.13 "type": "PlainIntegerRelationState", 10.68/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "446": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 11, 10.89/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T65", 10.89/4.13 "T66" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "326": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "447": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 11, 10.89/4.13 "term": "(log2 T66 (s (s (s (s (s (s (s (0)))))))) T65)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T65", 10.89/4.13 "T66" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "327": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "448": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "328": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 5, 10.89/4.13 "term": "(log2 T15 (s (0)) T13)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T13", 10.89/4.13 "T15" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "449": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "329": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 5, 10.89/4.13 "term": "(log2 T15 (s (0)) T13)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T13", 10.89/4.13 "T15" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "171": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "293": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": ["X35"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "295": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 4, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 5, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 6, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": ["X35"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "296": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 4, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": ["X35"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "450": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "297": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 5, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 6, 10.89/4.13 "scope": 4, 10.89/4.13 "term": "(half T20 X35)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": ["X35"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "330": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "451": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(',' (half (s (s T71)) X205) (log2 X205 (s (s (s (s (s (s (s (s (0))))))))) T72))" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T71", 10.89/4.13 "T72" 10.89/4.13 ], 10.89/4.13 "free": ["X205"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "331": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "452": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "332": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "453": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(',' (half (s (s T71)) X205) (log2 X205 (s T73) T72))" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T71", 10.89/4.13 "T72", 10.89/4.13 "T73" 10.89/4.13 ], 10.89/4.13 "free": ["X205"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "333": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(',' (half (s (s T29)) X67) (log2 X67 (s (s (0))) T30))" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T29", 10.89/4.13 "T30" 10.89/4.13 ], 10.89/4.13 "free": ["X67"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "454": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(half (s (s T71)) X205)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": ["T71"], 10.89/4.13 "free": ["X205"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "334": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "455": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "335": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(half (s (s T29)) X67)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": ["T29"], 10.89/4.13 "free": ["X67"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "456": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 1, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "336": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "457": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 1, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "337": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 1, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "458": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "338": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 1, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "459": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "339": { 10.89/4.13 "goal": [ 10.89/4.13 { 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }, 10.89/4.13 { 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 } 10.89/4.13 ], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "71": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(log2 T7 (0) T6)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": ["T6"], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "460": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "340": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "461": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "341": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "462": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "342": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "463": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 12, 10.89/4.13 "term": "(log2 T74 (s T73) T72)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T72", 10.89/4.13 "T73", 10.89/4.13 "T74" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "343": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 2, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "464": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "344": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": 3, 10.89/4.13 "scope": 6, 10.89/4.13 "term": "(log2 T31 (s (s (0))) T30)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T30", 10.89/4.13 "T31" 10.89/4.13 ], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "465": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "345": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(true)" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "466": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "346": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "347": { 10.89/4.13 "goal": [], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [], 10.89/4.13 "free": [], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "348": { 10.89/4.13 "goal": [{ 10.89/4.13 "clause": -1, 10.89/4.13 "scope": -1, 10.89/4.13 "term": "(',' (half (s (s T36)) X90) (log2 X90 (s (s (s (0)))) T37))" 10.89/4.13 }], 10.89/4.13 "kb": { 10.89/4.13 "nonunifying": [], 10.89/4.13 "intvars": {}, 10.89/4.13 "arithmetic": { 10.89/4.13 "type": "PlainIntegerRelationState", 10.89/4.13 "relations": [] 10.89/4.13 }, 10.89/4.13 "ground": [ 10.89/4.13 "T36", 10.89/4.13 "T37" 10.89/4.13 ], 10.89/4.13 "free": ["X90"], 10.89/4.13 "exprvars": [] 10.89/4.13 } 10.89/4.13 }, 10.89/4.13 "349": { 10.89/4.13 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "edges": [ 10.89/4.14 { 10.89/4.14 "from": 2, 10.89/4.14 "to": 19, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 19, 10.89/4.14 "to": 71, 10.89/4.14 "label": "ONLY EVAL with clause\nlog2(X4, X5) :- log2(X4, 0, X5).\nand substitutionT1 -> T7,\nX4 -> T7,\nT2 -> T6,\nX5 -> T6,\nT5 -> T7" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 71, 10.89/4.14 "to": 89, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 89, 10.89/4.14 "to": 90, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 89, 10.89/4.14 "to": 91, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 90, 10.89/4.14 "to": 93, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X10, X10).\nand substitutionT7 -> 0,\nX10 -> 0,\nT6 -> 0" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 90, 10.89/4.14 "to": 94, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 91, 10.89/4.14 "to": 147, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 91, 10.89/4.14 "to": 148, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 93, 10.89/4.14 "to": 96, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 147, 10.89/4.14 "to": 166, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X15, X15).\nand substitutionT7 -> s(0),\nX15 -> 0,\nT6 -> 0" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 147, 10.89/4.14 "to": 168, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 148, 10.89/4.14 "to": 283, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X23)), X24, X25) :- ','(half(s(s(X23)), X26), log2(X26, s(X24), X25)).\nand substitutionX23 -> T14,\nT7 -> s(s(T14)),\nX24 -> 0,\nT6 -> T13,\nX25 -> T13,\nT12 -> T14" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 148, 10.89/4.14 "to": 284, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 166, 10.89/4.14 "to": 171, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 283, 10.89/4.14 "to": 285, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 283, 10.89/4.14 "to": 286, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT14 is ground\nT15 is ground\nreplacements:X26 -> T15" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 285, 10.89/4.14 "to": 287, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 286, 10.89/4.14 "to": 321, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 287, 10.89/4.14 "to": 288, 10.89/4.14 "label": "BACKTRACK\nfor clause: half(0, 0)because of non-unification" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 288, 10.89/4.14 "to": 289, 10.89/4.14 "label": "BACKTRACK\nfor clause: half(s(0), 0)because of non-unification" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 289, 10.89/4.14 "to": 293, 10.89/4.14 "label": "ONLY EVAL with clause\nhalf(s(s(X33)), s(X34)) :- half(X33, X34).\nand substitutionT14 -> T20,\nX33 -> T20,\nX34 -> X35,\nX26 -> s(X35),\nT19 -> T20" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 293, 10.89/4.14 "to": 295, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 295, 10.89/4.14 "to": 296, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 295, 10.89/4.14 "to": 297, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 296, 10.89/4.14 "to": 301, 10.89/4.14 "label": "EVAL with clause\nhalf(0, 0).\nand substitutionT20 -> 0,\nX35 -> 0" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 296, 10.89/4.14 "to": 302, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 297, 10.89/4.14 "to": 307, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 297, 10.89/4.14 "to": 308, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 301, 10.89/4.14 "to": 303, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 307, 10.89/4.14 "to": 311, 10.89/4.14 "label": "EVAL with clause\nhalf(s(0), 0).\nand substitutionT20 -> s(0),\nX35 -> 0" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 307, 10.89/4.14 "to": 312, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 308, 10.89/4.14 "to": 317, 10.89/4.14 "label": "EVAL with clause\nhalf(s(s(X42)), s(X43)) :- half(X42, X43).\nand substitutionX42 -> T24,\nT20 -> s(s(T24)),\nX43 -> X44,\nX35 -> s(X44),\nT23 -> T24" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 308, 10.89/4.14 "to": 318, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 311, 10.89/4.14 "to": 314, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 317, 10.89/4.14 "to": 293, 10.89/4.14 "label": "INSTANCE with matching:\nT20 -> T24\nX35 -> X44" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 321, 10.89/4.14 "to": 322, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 321, 10.89/4.14 "to": 324, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 322, 10.89/4.14 "to": 325, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X51, X51).\nand substitutionT15 -> 0,\nX51 -> s(0),\nT13 -> s(0)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 322, 10.89/4.14 "to": 326, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 324, 10.89/4.14 "to": 328, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 324, 10.89/4.14 "to": 329, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 325, 10.89/4.14 "to": 327, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 328, 10.89/4.14 "to": 330, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X56, X56).\nand substitutionT15 -> s(0),\nX56 -> s(0),\nT13 -> s(0)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 328, 10.89/4.14 "to": 331, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 329, 10.89/4.14 "to": 333, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X64)), X65, X66) :- ','(half(s(s(X64)), X67), log2(X67, s(X65), X66)).\nand substitutionX64 -> T29,\nT15 -> s(s(T29)),\nX65 -> s(0),\nT13 -> T30,\nX66 -> T30" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 329, 10.89/4.14 "to": 334, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 330, 10.89/4.14 "to": 332, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 333, 10.89/4.14 "to": 335, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 333, 10.89/4.14 "to": 336, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT29 is ground\nT31 is ground\nreplacements:X67 -> T31" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 335, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T29\nX26 -> X67" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 336, 10.89/4.14 "to": 337, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 337, 10.89/4.14 "to": 338, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 337, 10.89/4.14 "to": 339, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 338, 10.89/4.14 "to": 340, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X74, X74).\nand substitutionT31 -> 0,\nX74 -> s(s(0)),\nT30 -> s(s(0))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 338, 10.89/4.14 "to": 341, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 339, 10.89/4.14 "to": 343, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 339, 10.89/4.14 "to": 344, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 340, 10.89/4.14 "to": 342, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 343, 10.89/4.14 "to": 345, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X79, X79).\nand substitutionT31 -> s(0),\nX79 -> s(s(0)),\nT30 -> s(s(0))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 343, 10.89/4.14 "to": 346, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 344, 10.89/4.14 "to": 348, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X87)), X88, X89) :- ','(half(s(s(X87)), X90), log2(X90, s(X88), X89)).\nand substitutionX87 -> T36,\nT31 -> s(s(T36)),\nX88 -> s(s(0)),\nT30 -> T37,\nX89 -> T37" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 344, 10.89/4.14 "to": 349, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 345, 10.89/4.14 "to": 347, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 348, 10.89/4.14 "to": 350, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 348, 10.89/4.14 "to": 351, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT36 is ground\nT38 is ground\nreplacements:X90 -> T38" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 350, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T36\nX26 -> X90" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 351, 10.89/4.14 "to": 352, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 352, 10.89/4.14 "to": 353, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 352, 10.89/4.14 "to": 354, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 353, 10.89/4.14 "to": 355, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X97, X97).\nand substitutionT38 -> 0,\nX97 -> s(s(s(0))),\nT37 -> s(s(s(0)))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 353, 10.89/4.14 "to": 356, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 354, 10.89/4.14 "to": 358, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 354, 10.89/4.14 "to": 359, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 355, 10.89/4.14 "to": 357, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 358, 10.89/4.14 "to": 360, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X102, X102).\nand substitutionT38 -> s(0),\nX102 -> s(s(s(0))),\nT37 -> s(s(s(0)))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 358, 10.89/4.14 "to": 361, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 359, 10.89/4.14 "to": 363, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X110)), X111, X112) :- ','(half(s(s(X110)), X113), log2(X113, s(X111), X112)).\nand substitutionX110 -> T43,\nT38 -> s(s(T43)),\nX111 -> s(s(s(0))),\nT37 -> T44,\nX112 -> T44" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 359, 10.89/4.14 "to": 364, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 360, 10.89/4.14 "to": 362, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 363, 10.89/4.14 "to": 365, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 363, 10.89/4.14 "to": 366, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT43 is ground\nT45 is ground\nreplacements:X113 -> T45" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 365, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T43\nX26 -> X113" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 366, 10.89/4.14 "to": 367, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 367, 10.89/4.14 "to": 368, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 367, 10.89/4.14 "to": 369, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 368, 10.89/4.14 "to": 370, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X120, X120).\nand substitutionT45 -> 0,\nX120 -> s(s(s(s(0)))),\nT44 -> s(s(s(s(0))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 368, 10.89/4.14 "to": 371, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 369, 10.89/4.14 "to": 373, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 369, 10.89/4.14 "to": 374, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 370, 10.89/4.14 "to": 372, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 373, 10.89/4.14 "to": 375, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X125, X125).\nand substitutionT45 -> s(0),\nX125 -> s(s(s(s(0)))),\nT44 -> s(s(s(s(0))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 373, 10.89/4.14 "to": 376, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 374, 10.89/4.14 "to": 378, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X133)), X134, X135) :- ','(half(s(s(X133)), X136), log2(X136, s(X134), X135)).\nand substitutionX133 -> T50,\nT45 -> s(s(T50)),\nX134 -> s(s(s(s(0)))),\nT44 -> T51,\nX135 -> T51" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 374, 10.89/4.14 "to": 379, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 375, 10.89/4.14 "to": 377, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 378, 10.89/4.14 "to": 380, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 378, 10.89/4.14 "to": 381, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT50 is ground\nT52 is ground\nreplacements:X136 -> T52" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 380, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T50\nX26 -> X136" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 381, 10.89/4.14 "to": 382, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 382, 10.89/4.14 "to": 383, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 382, 10.89/4.14 "to": 384, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 383, 10.89/4.14 "to": 385, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X143, X143).\nand substitutionT52 -> 0,\nX143 -> s(s(s(s(s(0))))),\nT51 -> s(s(s(s(s(0)))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 383, 10.89/4.14 "to": 386, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 384, 10.89/4.14 "to": 390, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 384, 10.89/4.14 "to": 391, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 385, 10.89/4.14 "to": 387, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 390, 10.89/4.14 "to": 395, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X148, X148).\nand substitutionT52 -> s(0),\nX148 -> s(s(s(s(s(0))))),\nT51 -> s(s(s(s(s(0)))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 390, 10.89/4.14 "to": 396, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 391, 10.89/4.14 "to": 403, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X156)), X157, X158) :- ','(half(s(s(X156)), X159), log2(X159, s(X157), X158)).\nand substitutionX156 -> T57,\nT52 -> s(s(T57)),\nX157 -> s(s(s(s(s(0))))),\nT51 -> T58,\nX158 -> T58" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 391, 10.89/4.14 "to": 404, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 395, 10.89/4.14 "to": 397, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 403, 10.89/4.14 "to": 406, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 403, 10.89/4.14 "to": 407, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT57 is ground\nT59 is ground\nreplacements:X159 -> T59" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 406, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T57\nX26 -> X159" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 407, 10.89/4.14 "to": 411, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 411, 10.89/4.14 "to": 412, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 411, 10.89/4.14 "to": 413, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 412, 10.89/4.14 "to": 414, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X166, X166).\nand substitutionT59 -> 0,\nX166 -> s(s(s(s(s(s(0)))))),\nT58 -> s(s(s(s(s(s(0))))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 412, 10.89/4.14 "to": 415, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 413, 10.89/4.14 "to": 417, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 413, 10.89/4.14 "to": 418, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 414, 10.89/4.14 "to": 416, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 417, 10.89/4.14 "to": 419, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X171, X171).\nand substitutionT59 -> s(0),\nX171 -> s(s(s(s(s(s(0)))))),\nT58 -> s(s(s(s(s(s(0))))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 417, 10.89/4.14 "to": 420, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 418, 10.89/4.14 "to": 422, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X179)), X180, X181) :- ','(half(s(s(X179)), X182), log2(X182, s(X180), X181)).\nand substitutionX179 -> T64,\nT59 -> s(s(T64)),\nX180 -> s(s(s(s(s(s(0)))))),\nT58 -> T65,\nX181 -> T65" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 418, 10.89/4.14 "to": 423, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 419, 10.89/4.14 "to": 421, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 422, 10.89/4.14 "to": 424, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 422, 10.89/4.14 "to": 425, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT64 is ground\nT66 is ground\nreplacements:X182 -> T66" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 424, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T64\nX26 -> X182" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 425, 10.89/4.14 "to": 440, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 440, 10.89/4.14 "to": 441, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 440, 10.89/4.14 "to": 442, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 441, 10.89/4.14 "to": 443, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X189, X189).\nand substitutionT66 -> 0,\nX189 -> s(s(s(s(s(s(s(0))))))),\nT65 -> s(s(s(s(s(s(s(0)))))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 441, 10.89/4.14 "to": 444, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 442, 10.89/4.14 "to": 446, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 442, 10.89/4.14 "to": 447, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 443, 10.89/4.14 "to": 445, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 446, 10.89/4.14 "to": 448, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X194, X194).\nand substitutionT66 -> s(0),\nX194 -> s(s(s(s(s(s(s(0))))))),\nT65 -> s(s(s(s(s(s(s(0)))))))" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 446, 10.89/4.14 "to": 449, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 447, 10.89/4.14 "to": 451, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X202)), X203, X204) :- ','(half(s(s(X202)), X205), log2(X205, s(X203), X204)).\nand substitutionX202 -> T71,\nT66 -> s(s(T71)),\nX203 -> s(s(s(s(s(s(s(0))))))),\nT65 -> T72,\nX204 -> T72" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 447, 10.89/4.14 "to": 452, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 448, 10.89/4.14 "to": 450, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 451, 10.89/4.14 "to": 453, 10.89/4.14 "label": "GENERALIZATION\nT73 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT73 is ground" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 453, 10.89/4.14 "to": 454, 10.89/4.14 "label": "SPLIT 1" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 453, 10.89/4.14 "to": 455, 10.89/4.14 "label": "SPLIT 2\nnew knowledge:\nT71 is ground\nT74 is ground\nreplacements:X205 -> T74" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 454, 10.89/4.14 "to": 285, 10.89/4.14 "label": "INSTANCE with matching:\nT14 -> T71\nX26 -> X205" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 455, 10.89/4.14 "to": 456, 10.89/4.14 "label": "CASE" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 456, 10.89/4.14 "to": 457, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 456, 10.89/4.14 "to": 458, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 457, 10.89/4.14 "to": 459, 10.89/4.14 "label": "EVAL with clause\nlog2(0, X212, X212).\nand substitutionT74 -> 0,\nT73 -> T81,\nX212 -> s(T81),\nT72 -> s(T81)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 457, 10.89/4.14 "to": 460, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 458, 10.89/4.14 "to": 462, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 458, 10.89/4.14 "to": 463, 10.89/4.14 "label": "PARALLEL" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 459, 10.89/4.14 "to": 461, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 462, 10.89/4.14 "to": 464, 10.89/4.14 "label": "EVAL with clause\nlog2(s(0), X217, X217).\nand substitutionT74 -> s(0),\nT73 -> T86,\nX217 -> s(T86),\nT72 -> s(T86)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 462, 10.89/4.14 "to": 465, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 463, 10.89/4.14 "to": 478, 10.89/4.14 "label": "EVAL with clause\nlog2(s(s(X225)), X226, X227) :- ','(half(s(s(X225)), X228), log2(X228, s(X226), X227)).\nand substitutionX225 -> T93,\nT74 -> s(s(T93)),\nT73 -> T94,\nX226 -> s(T94),\nT72 -> T95,\nX227 -> T95" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 463, 10.89/4.14 "to": 479, 10.89/4.14 "label": "EVAL-BACKTRACK" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 464, 10.89/4.14 "to": 466, 10.89/4.14 "label": "SUCCESS" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "from": 478, 10.89/4.14 "to": 453, 10.89/4.14 "label": "INSTANCE with matching:\nT71 -> T93\nX205 -> X228\nT73 -> s(T94)\nT72 -> T95" 10.89/4.14 } 10.89/4.14 ], 10.89/4.14 "type": "Graph" 10.89/4.14 } 10.89/4.14 } 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (56) 10.89/4.14 Obligation: 10.89/4.14 Triples: 10.89/4.14 10.89/4.14 halfA(s(s(X1)), s(X2)) :- halfA(X1, X2). 10.89/4.14 halfB(X1, s(X2)) :- halfA(X1, X2). 10.89/4.14 pC(X1, X2, X3, X4) :- halfB(X1, X2). 10.89/4.14 pC(X1, s(s(X2)), X3, X4) :- ','(halfcB(X1, s(s(X2))), pC(X2, X5, s(X3), X4)). 10.89/4.14 log2D(s(s(X1)), X2) :- halfB(X1, X3). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), halfB(X3, X4)). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), halfB(X4, X5))). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), ','(halfcB(X4, s(s(X5))), halfB(X5, X6)))). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), ','(halfcB(X4, s(s(X5))), ','(halfcB(X5, s(s(X6))), halfB(X6, X7))))). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), ','(halfcB(X4, s(s(X5))), ','(halfcB(X5, s(s(X6))), ','(halfcB(X6, s(s(X7))), halfB(X7, X8)))))). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), ','(halfcB(X4, s(s(X5))), ','(halfcB(X5, s(s(X6))), ','(halfcB(X6, s(s(X7))), ','(halfcB(X7, s(s(X8))), halfB(X8, X9))))))). 10.89/4.14 log2D(s(s(X1)), X2) :- ','(halfcB(X1, s(s(X3))), ','(halfcB(X3, s(s(X4))), ','(halfcB(X4, s(s(X5))), ','(halfcB(X5, s(s(X6))), ','(halfcB(X6, s(s(X7))), ','(halfcB(X7, s(s(X8))), ','(halfcB(X8, s(s(X9))), pC(X9, X10, s(s(s(s(s(s(s(0))))))), X2)))))))). 10.89/4.14 10.89/4.14 Clauses: 10.89/4.14 10.89/4.14 halfcA(0, 0). 10.89/4.14 halfcA(s(0), 0). 10.89/4.14 halfcA(s(s(X1)), s(X2)) :- halfcA(X1, X2). 10.89/4.14 halfcB(X1, s(X2)) :- halfcA(X1, X2). 10.89/4.14 qcC(X1, 0, X2, s(X2)) :- halfcB(X1, 0). 10.89/4.14 qcC(X1, s(0), X2, s(X2)) :- halfcB(X1, s(0)). 10.89/4.14 qcC(X1, s(s(X2)), X3, X4) :- ','(halfcB(X1, s(s(X2))), qcC(X2, X5, s(X3), X4)). 10.89/4.14 10.89/4.14 Afs: 10.89/4.14 10.89/4.14 log2D(x1, x2) = log2D(x2) 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (57) TriplesToPiDPProof (SOUND) 10.89/4.14 We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: 10.89/4.14 10.89/4.14 log2D_in_2: (f,b) 10.89/4.14 10.89/4.14 halfB_in_2: (f,f) (b,f) 10.89/4.14 10.89/4.14 halfA_in_2: (f,f) (b,f) 10.89/4.14 10.89/4.14 halfcB_in_2: (f,f) (b,f) 10.89/4.14 10.89/4.14 halfcA_in_2: (f,f) (b,f) 10.89/4.14 10.89/4.14 pC_in_4: (b,f,b,b) 10.89/4.14 10.89/4.14 Transforming TRIPLES into the following Term Rewriting System: 10.89/4.14 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> U6_AG(X1, X2, halfB_in_aa(X1, X3)) 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> HALFB_IN_AA(X1, X3) 10.89/4.14 HALFB_IN_AA(X1, s(X2)) -> U2_AA(X1, X2, halfA_in_aa(X1, X2)) 10.89/4.14 HALFB_IN_AA(X1, s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> U1_AA(X1, X2, halfA_in_aa(X1, X2)) 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> U7_AG(X1, X2, halfcB_in_aa(X1, s(s(X3)))) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> U8_AG(X1, X2, halfB_in_ga(X3, X4)) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> HALFB_IN_GA(X3, X4) 10.89/4.14 HALFB_IN_GA(X1, s(X2)) -> U2_GA(X1, X2, halfA_in_ga(X1, X2)) 10.89/4.14 HALFB_IN_GA(X1, s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> U1_GA(X1, X2, halfA_in_ga(X1, X2)) 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> U9_AG(X1, X2, halfcB_in_ga(X3, s(s(X4)))) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> U10_AG(X1, X2, halfB_in_ga(X4, X5)) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> HALFB_IN_GA(X4, X5) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> U11_AG(X1, X2, halfcB_in_ga(X4, s(s(X5)))) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> U12_AG(X1, X2, halfB_in_ga(X5, X6)) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> HALFB_IN_GA(X5, X6) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> U13_AG(X1, X2, halfcB_in_ga(X5, s(s(X6)))) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> U14_AG(X1, X2, halfB_in_ga(X6, X7)) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> HALFB_IN_GA(X6, X7) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> U15_AG(X1, X2, halfcB_in_ga(X6, s(s(X7)))) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> U16_AG(X1, X2, halfB_in_ga(X7, X8)) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> HALFB_IN_GA(X7, X8) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> U17_AG(X1, X2, halfcB_in_ga(X7, s(s(X8)))) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> U18_AG(X1, X2, halfB_in_ga(X8, X9)) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> HALFB_IN_GA(X8, X9) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> U19_AG(X1, X2, halfcB_in_ga(X8, s(s(X9)))) 10.89/4.14 U19_AG(X1, X2, halfcB_out_ga(X8, s(s(X9)))) -> U20_AG(X1, X2, pC_in_gagg(X9, X10, s(s(s(s(s(s(s(0))))))), X2)) 10.89/4.14 U19_AG(X1, X2, halfcB_out_ga(X8, s(s(X9)))) -> PC_IN_GAGG(X9, X10, s(s(s(s(s(s(s(0))))))), X2) 10.89/4.14 PC_IN_GAGG(X1, X2, X3, X4) -> U3_GAGG(X1, X2, X3, X4, halfB_in_ga(X1, X2)) 10.89/4.14 PC_IN_GAGG(X1, X2, X3, X4) -> HALFB_IN_GA(X1, X2) 10.89/4.14 PC_IN_GAGG(X1, s(s(X2)), X3, X4) -> U4_GAGG(X1, X2, X3, X4, halfcB_in_ga(X1, s(s(X2)))) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> U5_GAGG(X1, X2, X3, X4, pC_in_gagg(X2, X5, s(X3), X4)) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, X5, s(X3), X4) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_aa(X1, s(X2)) -> U23_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 halfcA_in_aa(0, 0) -> halfcA_out_aa(0, 0) 10.89/4.14 halfcA_in_aa(s(0), 0) -> halfcA_out_aa(s(0), 0) 10.89/4.14 halfcA_in_aa(s(s(X1)), s(X2)) -> U22_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 U22_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcA_out_aa(s(s(X1)), s(X2)) 10.89/4.14 U23_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcB_out_aa(X1, s(X2)) 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 halfB_in_aa(x1, x2) = halfB_in_aa 10.89/4.14 10.89/4.14 halfA_in_aa(x1, x2) = halfA_in_aa 10.89/4.14 10.89/4.14 halfcB_in_aa(x1, x2) = halfcB_in_aa 10.89/4.14 10.89/4.14 U23_aa(x1, x2, x3) = U23_aa(x3) 10.89/4.14 10.89/4.14 halfcA_in_aa(x1, x2) = halfcA_in_aa 10.89/4.14 10.89/4.14 halfcA_out_aa(x1, x2) = halfcA_out_aa(x1, x2) 10.89/4.14 10.89/4.14 U22_aa(x1, x2, x3) = U22_aa(x3) 10.89/4.14 10.89/4.14 halfcB_out_aa(x1, x2) = halfcB_out_aa(x1, x2) 10.89/4.14 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfB_in_ga(x1, x2) = halfB_in_ga(x1) 10.89/4.14 10.89/4.14 halfA_in_ga(x1, x2) = halfA_in_ga(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 pC_in_gagg(x1, x2, x3, x4) = pC_in_gagg(x1, x3, x4) 10.89/4.14 10.89/4.14 LOG2D_IN_AG(x1, x2) = LOG2D_IN_AG(x2) 10.89/4.14 10.89/4.14 U6_AG(x1, x2, x3) = U6_AG(x2, x3) 10.89/4.14 10.89/4.14 HALFB_IN_AA(x1, x2) = HALFB_IN_AA 10.89/4.14 10.89/4.14 U2_AA(x1, x2, x3) = U2_AA(x3) 10.89/4.14 10.89/4.14 HALFA_IN_AA(x1, x2) = HALFA_IN_AA 10.89/4.14 10.89/4.14 U1_AA(x1, x2, x3) = U1_AA(x3) 10.89/4.14 10.89/4.14 U7_AG(x1, x2, x3) = U7_AG(x2, x3) 10.89/4.14 10.89/4.14 U8_AG(x1, x2, x3) = U8_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 HALFB_IN_GA(x1, x2) = HALFB_IN_GA(x1) 10.89/4.14 10.89/4.14 U2_GA(x1, x2, x3) = U2_GA(x1, x3) 10.89/4.14 10.89/4.14 HALFA_IN_GA(x1, x2) = HALFA_IN_GA(x1) 10.89/4.14 10.89/4.14 U1_GA(x1, x2, x3) = U1_GA(x1, x3) 10.89/4.14 10.89/4.14 U9_AG(x1, x2, x3) = U9_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U10_AG(x1, x2, x3) = U10_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U11_AG(x1, x2, x3) = U11_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U12_AG(x1, x2, x3) = U12_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U13_AG(x1, x2, x3) = U13_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U14_AG(x1, x2, x3) = U14_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U15_AG(x1, x2, x3) = U15_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U16_AG(x1, x2, x3) = U16_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U17_AG(x1, x2, x3) = U17_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U18_AG(x1, x2, x3) = U18_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U19_AG(x1, x2, x3) = U19_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U20_AG(x1, x2, x3) = U20_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 PC_IN_GAGG(x1, x2, x3, x4) = PC_IN_GAGG(x1, x3, x4) 10.89/4.14 10.89/4.14 U3_GAGG(x1, x2, x3, x4, x5) = U3_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 U4_GAGG(x1, x2, x3, x4, x5) = U4_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 U5_GAGG(x1, x2, x3, x4, x5) = U5_GAGG(x1, x2, x3, x4, x5) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 10.89/4.14 10.89/4.14 Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES 10.89/4.14 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (58) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> U6_AG(X1, X2, halfB_in_aa(X1, X3)) 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> HALFB_IN_AA(X1, X3) 10.89/4.14 HALFB_IN_AA(X1, s(X2)) -> U2_AA(X1, X2, halfA_in_aa(X1, X2)) 10.89/4.14 HALFB_IN_AA(X1, s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> U1_AA(X1, X2, halfA_in_aa(X1, X2)) 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 LOG2D_IN_AG(s(s(X1)), X2) -> U7_AG(X1, X2, halfcB_in_aa(X1, s(s(X3)))) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> U8_AG(X1, X2, halfB_in_ga(X3, X4)) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> HALFB_IN_GA(X3, X4) 10.89/4.14 HALFB_IN_GA(X1, s(X2)) -> U2_GA(X1, X2, halfA_in_ga(X1, X2)) 10.89/4.14 HALFB_IN_GA(X1, s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> U1_GA(X1, X2, halfA_in_ga(X1, X2)) 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 U7_AG(X1, X2, halfcB_out_aa(X1, s(s(X3)))) -> U9_AG(X1, X2, halfcB_in_ga(X3, s(s(X4)))) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> U10_AG(X1, X2, halfB_in_ga(X4, X5)) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> HALFB_IN_GA(X4, X5) 10.89/4.14 U9_AG(X1, X2, halfcB_out_ga(X3, s(s(X4)))) -> U11_AG(X1, X2, halfcB_in_ga(X4, s(s(X5)))) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> U12_AG(X1, X2, halfB_in_ga(X5, X6)) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> HALFB_IN_GA(X5, X6) 10.89/4.14 U11_AG(X1, X2, halfcB_out_ga(X4, s(s(X5)))) -> U13_AG(X1, X2, halfcB_in_ga(X5, s(s(X6)))) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> U14_AG(X1, X2, halfB_in_ga(X6, X7)) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> HALFB_IN_GA(X6, X7) 10.89/4.14 U13_AG(X1, X2, halfcB_out_ga(X5, s(s(X6)))) -> U15_AG(X1, X2, halfcB_in_ga(X6, s(s(X7)))) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> U16_AG(X1, X2, halfB_in_ga(X7, X8)) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> HALFB_IN_GA(X7, X8) 10.89/4.14 U15_AG(X1, X2, halfcB_out_ga(X6, s(s(X7)))) -> U17_AG(X1, X2, halfcB_in_ga(X7, s(s(X8)))) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> U18_AG(X1, X2, halfB_in_ga(X8, X9)) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> HALFB_IN_GA(X8, X9) 10.89/4.14 U17_AG(X1, X2, halfcB_out_ga(X7, s(s(X8)))) -> U19_AG(X1, X2, halfcB_in_ga(X8, s(s(X9)))) 10.89/4.14 U19_AG(X1, X2, halfcB_out_ga(X8, s(s(X9)))) -> U20_AG(X1, X2, pC_in_gagg(X9, X10, s(s(s(s(s(s(s(0))))))), X2)) 10.89/4.14 U19_AG(X1, X2, halfcB_out_ga(X8, s(s(X9)))) -> PC_IN_GAGG(X9, X10, s(s(s(s(s(s(s(0))))))), X2) 10.89/4.14 PC_IN_GAGG(X1, X2, X3, X4) -> U3_GAGG(X1, X2, X3, X4, halfB_in_ga(X1, X2)) 10.89/4.14 PC_IN_GAGG(X1, X2, X3, X4) -> HALFB_IN_GA(X1, X2) 10.89/4.14 PC_IN_GAGG(X1, s(s(X2)), X3, X4) -> U4_GAGG(X1, X2, X3, X4, halfcB_in_ga(X1, s(s(X2)))) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> U5_GAGG(X1, X2, X3, X4, pC_in_gagg(X2, X5, s(X3), X4)) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, X5, s(X3), X4) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_aa(X1, s(X2)) -> U23_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 halfcA_in_aa(0, 0) -> halfcA_out_aa(0, 0) 10.89/4.14 halfcA_in_aa(s(0), 0) -> halfcA_out_aa(s(0), 0) 10.89/4.14 halfcA_in_aa(s(s(X1)), s(X2)) -> U22_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 U22_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcA_out_aa(s(s(X1)), s(X2)) 10.89/4.14 U23_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcB_out_aa(X1, s(X2)) 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 halfB_in_aa(x1, x2) = halfB_in_aa 10.89/4.14 10.89/4.14 halfA_in_aa(x1, x2) = halfA_in_aa 10.89/4.14 10.89/4.14 halfcB_in_aa(x1, x2) = halfcB_in_aa 10.89/4.14 10.89/4.14 U23_aa(x1, x2, x3) = U23_aa(x3) 10.89/4.14 10.89/4.14 halfcA_in_aa(x1, x2) = halfcA_in_aa 10.89/4.14 10.89/4.14 halfcA_out_aa(x1, x2) = halfcA_out_aa(x1, x2) 10.89/4.14 10.89/4.14 U22_aa(x1, x2, x3) = U22_aa(x3) 10.89/4.14 10.89/4.14 halfcB_out_aa(x1, x2) = halfcB_out_aa(x1, x2) 10.89/4.14 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfB_in_ga(x1, x2) = halfB_in_ga(x1) 10.89/4.14 10.89/4.14 halfA_in_ga(x1, x2) = halfA_in_ga(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 pC_in_gagg(x1, x2, x3, x4) = pC_in_gagg(x1, x3, x4) 10.89/4.14 10.89/4.14 LOG2D_IN_AG(x1, x2) = LOG2D_IN_AG(x2) 10.89/4.14 10.89/4.14 U6_AG(x1, x2, x3) = U6_AG(x2, x3) 10.89/4.14 10.89/4.14 HALFB_IN_AA(x1, x2) = HALFB_IN_AA 10.89/4.14 10.89/4.14 U2_AA(x1, x2, x3) = U2_AA(x3) 10.89/4.14 10.89/4.14 HALFA_IN_AA(x1, x2) = HALFA_IN_AA 10.89/4.14 10.89/4.14 U1_AA(x1, x2, x3) = U1_AA(x3) 10.89/4.14 10.89/4.14 U7_AG(x1, x2, x3) = U7_AG(x2, x3) 10.89/4.14 10.89/4.14 U8_AG(x1, x2, x3) = U8_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 HALFB_IN_GA(x1, x2) = HALFB_IN_GA(x1) 10.89/4.14 10.89/4.14 U2_GA(x1, x2, x3) = U2_GA(x1, x3) 10.89/4.14 10.89/4.14 HALFA_IN_GA(x1, x2) = HALFA_IN_GA(x1) 10.89/4.14 10.89/4.14 U1_GA(x1, x2, x3) = U1_GA(x1, x3) 10.89/4.14 10.89/4.14 U9_AG(x1, x2, x3) = U9_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U10_AG(x1, x2, x3) = U10_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U11_AG(x1, x2, x3) = U11_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U12_AG(x1, x2, x3) = U12_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U13_AG(x1, x2, x3) = U13_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U14_AG(x1, x2, x3) = U14_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U15_AG(x1, x2, x3) = U15_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U16_AG(x1, x2, x3) = U16_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U17_AG(x1, x2, x3) = U17_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U18_AG(x1, x2, x3) = U18_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U19_AG(x1, x2, x3) = U19_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 U20_AG(x1, x2, x3) = U20_AG(x1, x2, x3) 10.89/4.14 10.89/4.14 PC_IN_GAGG(x1, x2, x3, x4) = PC_IN_GAGG(x1, x3, x4) 10.89/4.14 10.89/4.14 U3_GAGG(x1, x2, x3, x4, x5) = U3_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 U4_GAGG(x1, x2, x3, x4, x5) = U4_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 U5_GAGG(x1, x2, x3, x4, x5) = U5_GAGG(x1, x2, x3, x4, x5) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (59) DependencyGraphProof (EQUIVALENT) 10.89/4.14 The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 32 less nodes. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (60) 10.89/4.14 Complex Obligation (AND) 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (61) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_aa(X1, s(X2)) -> U23_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 halfcA_in_aa(0, 0) -> halfcA_out_aa(0, 0) 10.89/4.14 halfcA_in_aa(s(0), 0) -> halfcA_out_aa(s(0), 0) 10.89/4.14 halfcA_in_aa(s(s(X1)), s(X2)) -> U22_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 U22_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcA_out_aa(s(s(X1)), s(X2)) 10.89/4.14 U23_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcB_out_aa(X1, s(X2)) 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 halfcB_in_aa(x1, x2) = halfcB_in_aa 10.89/4.14 10.89/4.14 U23_aa(x1, x2, x3) = U23_aa(x3) 10.89/4.14 10.89/4.14 halfcA_in_aa(x1, x2) = halfcA_in_aa 10.89/4.14 10.89/4.14 halfcA_out_aa(x1, x2) = halfcA_out_aa(x1, x2) 10.89/4.14 10.89/4.14 U22_aa(x1, x2, x3) = U22_aa(x3) 10.89/4.14 10.89/4.14 halfcB_out_aa(x1, x2) = halfcB_out_aa(x1, x2) 10.89/4.14 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 HALFA_IN_GA(x1, x2) = HALFA_IN_GA(x1) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (62) UsableRulesProof (EQUIVALENT) 10.89/4.14 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (63) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_GA(s(s(X1)), s(X2)) -> HALFA_IN_GA(X1, X2) 10.89/4.14 10.89/4.14 R is empty. 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 HALFA_IN_GA(x1, x2) = HALFA_IN_GA(x1) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (64) PiDPToQDPProof (SOUND) 10.89/4.14 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (65) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_GA(s(s(X1))) -> HALFA_IN_GA(X1) 10.89/4.14 10.89/4.14 R is empty. 10.89/4.14 Q is empty. 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (66) QDPSizeChangeProof (EQUIVALENT) 10.89/4.14 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. 10.89/4.14 10.89/4.14 From the DPs we obtained the following set of size-change graphs: 10.89/4.14 *HALFA_IN_GA(s(s(X1))) -> HALFA_IN_GA(X1) 10.89/4.14 The graph contains the following edges 1 > 1 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (67) 10.89/4.14 YES 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (68) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 PC_IN_GAGG(X1, s(s(X2)), X3, X4) -> U4_GAGG(X1, X2, X3, X4, halfcB_in_ga(X1, s(s(X2)))) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, X5, s(X3), X4) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_aa(X1, s(X2)) -> U23_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 halfcA_in_aa(0, 0) -> halfcA_out_aa(0, 0) 10.89/4.14 halfcA_in_aa(s(0), 0) -> halfcA_out_aa(s(0), 0) 10.89/4.14 halfcA_in_aa(s(s(X1)), s(X2)) -> U22_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 U22_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcA_out_aa(s(s(X1)), s(X2)) 10.89/4.14 U23_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcB_out_aa(X1, s(X2)) 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 halfcB_in_aa(x1, x2) = halfcB_in_aa 10.89/4.14 10.89/4.14 U23_aa(x1, x2, x3) = U23_aa(x3) 10.89/4.14 10.89/4.14 halfcA_in_aa(x1, x2) = halfcA_in_aa 10.89/4.14 10.89/4.14 halfcA_out_aa(x1, x2) = halfcA_out_aa(x1, x2) 10.89/4.14 10.89/4.14 U22_aa(x1, x2, x3) = U22_aa(x3) 10.89/4.14 10.89/4.14 halfcB_out_aa(x1, x2) = halfcB_out_aa(x1, x2) 10.89/4.14 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 PC_IN_GAGG(x1, x2, x3, x4) = PC_IN_GAGG(x1, x3, x4) 10.89/4.14 10.89/4.14 U4_GAGG(x1, x2, x3, x4, x5) = U4_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (69) UsableRulesProof (EQUIVALENT) 10.89/4.14 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (70) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 PC_IN_GAGG(X1, s(s(X2)), X3, X4) -> U4_GAGG(X1, X2, X3, X4, halfcB_in_ga(X1, s(s(X2)))) 10.89/4.14 U4_GAGG(X1, X2, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, X5, s(X3), X4) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 PC_IN_GAGG(x1, x2, x3, x4) = PC_IN_GAGG(x1, x3, x4) 10.89/4.14 10.89/4.14 U4_GAGG(x1, x2, x3, x4, x5) = U4_GAGG(x1, x3, x4, x5) 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (71) PiDPToQDPProof (SOUND) 10.89/4.14 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (72) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, halfcB_in_ga(X1)) 10.89/4.14 U4_GAGG(X1, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, s(X3), X4) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_ga(X1) -> U23_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The set Q consists of the following terms: 10.89/4.14 10.89/4.14 halfcB_in_ga(x0) 10.89/4.14 U23_ga(x0, x1) 10.89/4.14 halfcA_in_ga(x0) 10.89/4.14 U22_ga(x0, x1) 10.89/4.14 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (73) TransformationProof (EQUIVALENT) 10.89/4.14 By rewriting [LPAR04] the rule PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, halfcB_in_ga(X1)) at position [3] we obtained the following new rules [LPAR04]: 10.89/4.14 10.89/4.14 (PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1))),PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1)))) 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (74) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 U4_GAGG(X1, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, s(X3), X4) 10.89/4.14 PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1))) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_ga(X1) -> U23_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The set Q consists of the following terms: 10.89/4.14 10.89/4.14 halfcB_in_ga(x0) 10.89/4.14 U23_ga(x0, x1) 10.89/4.14 halfcA_in_ga(x0) 10.89/4.14 U22_ga(x0, x1) 10.89/4.14 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (75) UsableRulesProof (EQUIVALENT) 10.89/4.14 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (76) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 U4_GAGG(X1, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, s(X3), X4) 10.89/4.14 PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1))) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The set Q consists of the following terms: 10.89/4.14 10.89/4.14 halfcB_in_ga(x0) 10.89/4.14 U23_ga(x0, x1) 10.89/4.14 halfcA_in_ga(x0) 10.89/4.14 U22_ga(x0, x1) 10.89/4.14 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (77) QReductionProof (EQUIVALENT) 10.89/4.14 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 10.89/4.14 10.89/4.14 halfcB_in_ga(x0) 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (78) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 U4_GAGG(X1, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, s(X3), X4) 10.89/4.14 PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1))) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The set Q consists of the following terms: 10.89/4.14 10.89/4.14 U23_ga(x0, x1) 10.89/4.14 halfcA_in_ga(x0) 10.89/4.14 U22_ga(x0, x1) 10.89/4.14 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (79) QDPOrderProof (EQUIVALENT) 10.89/4.14 We use the reduction pair processor [LPAR04,JAR06]. 10.89/4.14 10.89/4.14 10.89/4.14 The following pairs can be oriented strictly and are deleted. 10.89/4.14 10.89/4.14 U4_GAGG(X1, X3, X4, halfcB_out_ga(X1, s(s(X2)))) -> PC_IN_GAGG(X2, s(X3), X4) 10.89/4.14 PC_IN_GAGG(X1, X3, X4) -> U4_GAGG(X1, X3, X4, U23_ga(X1, halfcA_in_ga(X1))) 10.89/4.14 The remaining pairs can at least be oriented weakly. 10.89/4.14 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 10.89/4.14 10.89/4.14 POL( U23_ga_2(x_1, x_2) ) = max{0, 2x_2 - 2} 10.89/4.14 POL( U4_GAGG_4(x_1, ..., x_4) ) = max{0, x_4 - 2} 10.89/4.14 POL( halfcA_in_ga_1(x_1) ) = x_1 + 2 10.89/4.14 POL( 0 ) = 0 10.89/4.14 POL( halfcA_out_ga_2(x_1, x_2) ) = x_2 + 2 10.89/4.14 POL( s_1(x_1) ) = x_1 + 2 10.89/4.14 POL( U22_ga_2(x_1, x_2) ) = x_2 + 2 10.89/4.14 POL( halfcB_out_ga_2(x_1, x_2) ) = max{0, 2x_2 - 2} 10.89/4.14 POL( PC_IN_GAGG_3(x_1, ..., x_3) ) = 2x_1 + 1 10.89/4.14 10.89/4.14 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 10.89/4.14 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (80) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 P is empty. 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcA_in_ga(0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0)) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1))) -> U22_ga(X1, halfcA_in_ga(X1)) 10.89/4.14 U23_ga(X1, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 U22_ga(X1, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 10.89/4.14 The set Q consists of the following terms: 10.89/4.14 10.89/4.14 U23_ga(x0, x1) 10.89/4.14 halfcA_in_ga(x0) 10.89/4.14 U22_ga(x0, x1) 10.89/4.14 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (81) PisEmptyProof (EQUIVALENT) 10.89/4.14 The TRS P is empty. Hence, there is no (P,Q,R) chain. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (82) 10.89/4.14 YES 10.89/4.14 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (83) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 10.89/4.14 The TRS R consists of the following rules: 10.89/4.14 10.89/4.14 halfcB_in_aa(X1, s(X2)) -> U23_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 halfcA_in_aa(0, 0) -> halfcA_out_aa(0, 0) 10.89/4.14 halfcA_in_aa(s(0), 0) -> halfcA_out_aa(s(0), 0) 10.89/4.14 halfcA_in_aa(s(s(X1)), s(X2)) -> U22_aa(X1, X2, halfcA_in_aa(X1, X2)) 10.89/4.14 U22_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcA_out_aa(s(s(X1)), s(X2)) 10.89/4.14 U23_aa(X1, X2, halfcA_out_aa(X1, X2)) -> halfcB_out_aa(X1, s(X2)) 10.89/4.14 halfcB_in_ga(X1, s(X2)) -> U23_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 halfcA_in_ga(0, 0) -> halfcA_out_ga(0, 0) 10.89/4.14 halfcA_in_ga(s(0), 0) -> halfcA_out_ga(s(0), 0) 10.89/4.14 halfcA_in_ga(s(s(X1)), s(X2)) -> U22_ga(X1, X2, halfcA_in_ga(X1, X2)) 10.89/4.14 U22_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcA_out_ga(s(s(X1)), s(X2)) 10.89/4.14 U23_ga(X1, X2, halfcA_out_ga(X1, X2)) -> halfcB_out_ga(X1, s(X2)) 10.89/4.14 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 halfcB_in_aa(x1, x2) = halfcB_in_aa 10.89/4.14 10.89/4.14 U23_aa(x1, x2, x3) = U23_aa(x3) 10.89/4.14 10.89/4.14 halfcA_in_aa(x1, x2) = halfcA_in_aa 10.89/4.14 10.89/4.14 halfcA_out_aa(x1, x2) = halfcA_out_aa(x1, x2) 10.89/4.14 10.89/4.14 U22_aa(x1, x2, x3) = U22_aa(x3) 10.89/4.14 10.89/4.14 halfcB_out_aa(x1, x2) = halfcB_out_aa(x1, x2) 10.89/4.14 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 halfcB_in_ga(x1, x2) = halfcB_in_ga(x1) 10.89/4.14 10.89/4.14 U23_ga(x1, x2, x3) = U23_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcA_in_ga(x1, x2) = halfcA_in_ga(x1) 10.89/4.14 10.89/4.14 0 = 0 10.89/4.14 10.89/4.14 halfcA_out_ga(x1, x2) = halfcA_out_ga(x1, x2) 10.89/4.14 10.89/4.14 U22_ga(x1, x2, x3) = U22_ga(x1, x3) 10.89/4.14 10.89/4.14 halfcB_out_ga(x1, x2) = halfcB_out_ga(x1, x2) 10.89/4.14 10.89/4.14 HALFA_IN_AA(x1, x2) = HALFA_IN_AA 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (84) UsableRulesProof (EQUIVALENT) 10.89/4.14 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (85) 10.89/4.14 Obligation: 10.89/4.14 Pi DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_AA(s(s(X1)), s(X2)) -> HALFA_IN_AA(X1, X2) 10.89/4.14 10.89/4.14 R is empty. 10.89/4.14 The argument filtering Pi contains the following mapping: 10.89/4.14 s(x1) = s(x1) 10.89/4.14 10.89/4.14 HALFA_IN_AA(x1, x2) = HALFA_IN_AA 10.89/4.14 10.89/4.14 10.89/4.14 We have to consider all (P,R,Pi)-chains 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (86) PiDPToQDPProof (SOUND) 10.89/4.14 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (87) 10.89/4.14 Obligation: 10.89/4.14 Q DP problem: 10.89/4.14 The TRS P consists of the following rules: 10.89/4.14 10.89/4.14 HALFA_IN_AA -> HALFA_IN_AA 10.89/4.14 10.89/4.14 R is empty. 10.89/4.14 Q is empty. 10.89/4.14 We have to consider all (P,Q,R)-chains. 10.89/4.14 ---------------------------------------- 10.89/4.14 10.89/4.14 (88) PrologToTRSTransformerProof (SOUND) 10.89/4.14 Transformed Prolog program to TRS. 10.89/4.14 10.89/4.14 { 10.89/4.14 "root": 22, 10.89/4.14 "program": { 10.89/4.14 "directives": [], 10.89/4.14 "clauses": [ 10.89/4.14 [ 10.89/4.14 "(log2 X Y)", 10.89/4.14 "(log2 X (0) Y)" 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(log2 (0) I I)", 10.89/4.14 null 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(log2 (s (0)) I I)", 10.89/4.14 null 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(log2 (s (s X)) I Y)", 10.89/4.14 "(',' (half (s (s X)) X1) (log2 X1 (s I) Y))" 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(half (0) (0))", 10.89/4.14 null 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(half (s (0)) (0))", 10.89/4.14 null 10.89/4.14 ], 10.89/4.14 [ 10.89/4.14 "(half (s (s X)) (s Y))", 10.89/4.14 "(half X Y)" 10.89/4.14 ] 10.89/4.14 ] 10.89/4.14 }, 10.89/4.14 "graph": { 10.89/4.14 "nodes": { 10.89/4.14 "type": "Nodes", 10.89/4.14 "590": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 3, 10.89/4.14 "scope": 10, 10.89/4.14 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T53", 10.89/4.14 "T54" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "470": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 2, 10.89/4.14 "scope": 5, 10.89/4.14 "term": "(log2 T18 (s (0)) T16)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T16", 10.89/4.14 "T18" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "591": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(true)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "471": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 3, 10.89/4.14 "scope": 5, 10.89/4.14 "term": "(log2 T18 (s (0)) T16)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T16", 10.89/4.14 "T18" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "592": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "593": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "594": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(',' (half (s (s T59)) X160) (log2 X160 (s (s (s (s (s (0)))))) T60))" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T59", 10.89/4.14 "T60" 10.89/4.14 ], 10.89/4.14 "free": ["X160"], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "595": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "475": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(true)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "596": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(half (s (s T59)) X160)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": ["T59"], 10.89/4.14 "free": ["X160"], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "476": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "597": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T60", 10.89/4.14 "T61" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "477": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "598": { 10.89/4.14 "goal": [ 10.89/4.14 { 10.89/4.14 "clause": 1, 10.89/4.14 "scope": 11, 10.89/4.14 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "clause": 2, 10.89/4.14 "scope": 11, 10.89/4.14 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.14 }, 10.89/4.14 { 10.89/4.14 "clause": 3, 10.89/4.14 "scope": 11, 10.89/4.14 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.14 } 10.89/4.14 ], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T60", 10.89/4.14 "T61" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "511": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(true)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "599": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 1, 10.89/4.14 "scope": 11, 10.89/4.14 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T60", 10.89/4.14 "T61" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "632": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 2, 10.89/4.14 "scope": 12, 10.89/4.14 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T67", 10.89/4.14 "T68" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "512": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "514": { 10.89/4.14 "goal": [], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "635": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": 3, 10.89/4.14 "scope": 12, 10.89/4.14 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": [ 10.89/4.14 "T67", 10.89/4.14 "T68" 10.89/4.14 ], 10.89/4.14 "free": [], 10.89/4.14 "exprvars": [] 10.89/4.14 } 10.89/4.14 }, 10.89/4.14 "519": { 10.89/4.14 "goal": [{ 10.89/4.14 "clause": -1, 10.89/4.14 "scope": -1, 10.89/4.14 "term": "(half T40 X91)" 10.89/4.14 }], 10.89/4.14 "kb": { 10.89/4.14 "nonunifying": [], 10.89/4.14 "intvars": {}, 10.89/4.14 "arithmetic": { 10.89/4.14 "type": "PlainIntegerRelationState", 10.89/4.14 "relations": [] 10.89/4.14 }, 10.89/4.14 "ground": ["T40"], 10.89/4.15 "free": ["X91"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "97": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T9"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "481": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T32)) X73) (log2 X73 (s (s (0))) T33))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T32", 10.89/4.15 "T33" 10.89/4.15 ], 10.89/4.15 "free": ["X73"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "240": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "482": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "241": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "242": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "486": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T32"], 10.89/4.15 "free": ["X73"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "124": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 2, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T9"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "245": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T17)) X32) (log2 X32 (s (0)) T16))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T16"], 10.89/4.15 "free": ["X32"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "487": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "520": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "246": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "247": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X32"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "248": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T16", 10.89/4.15 "T18" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "129": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 2, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 2, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T9"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "526": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "527": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "528": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "22": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T1 T2)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T2"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "23": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 0, 10.89/4.15 "scope": 1, 10.89/4.15 "term": "(log2 T1 T2)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T2"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "493": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 4, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T32"], 10.89/4.15 "free": ["X73"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "495": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T32"], 10.89/4.15 "free": ["X73"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "497": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 6, 10.89/4.15 "term": "(half (s (s T32)) X73)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T32"], 10.89/4.15 "free": ["X73"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "531": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "532": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "533": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "654": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "534": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "655": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "535": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 8, 10.89/4.15 "term": "(log2 T34 (s (s (0))) T33)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T33", 10.89/4.15 "T34" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "656": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "657": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T73)) X206) (log2 X206 (s (s (s (s (s (s (s (0)))))))) T74))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T73", 10.89/4.15 "T74" 10.89/4.15 ], 10.89/4.15 "free": ["X206"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "658": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "538": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "539": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "540": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "541": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T45)) X114) (log2 X114 (s (s (s (0)))) T46))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T45", 10.89/4.15 "T46" 10.89/4.15 ], 10.89/4.15 "free": ["X114"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "300": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "388": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T16", 10.89/4.15 "T18" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "389": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T16", 10.89/4.15 "T18" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "543": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "304": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "305": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "701": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T80)) X229) (log2 X229 (s (s (s (s (s (s (s (s (0))))))))) T81))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T80", 10.89/4.15 "T81" 10.89/4.15 ], 10.89/4.15 "free": ["X229"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "306": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "702": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "309": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "706": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T80)) X229) (log2 X229 (s T82) T81))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T80", 10.89/4.15 "T81", 10.89/4.15 "T82" 10.89/4.15 ], 10.89/4.15 "free": ["X229"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "709": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half (s (s T80)) X229)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T80"], 10.89/4.15 "free": ["X229"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "310": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "673": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half (s (s T73)) X206)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T73"], 10.89/4.15 "free": ["X206"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "674": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "158": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "313": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "315": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "678": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "711": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "316": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "713": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "714": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "319": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half T27 X50)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X50"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "715": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "719": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "162": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "163": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "681": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "682": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "320": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "683": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "684": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "685": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "169": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 2, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T9"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "323": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 5, 10.89/4.15 "term": "(log2 T18 (s (0)) T16)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T16", 10.89/4.15 "T18" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "566": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half (s (s T45)) X114)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T45"], 10.89/4.15 "free": ["X114"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "720": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "567": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T46", 10.89/4.15 "T47" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "600": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 11, 10.89/4.15 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 11, 10.89/4.15 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T60", 10.89/4.15 "T61" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "688": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "721": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "568": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T46", 10.89/4.15 "T47" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "601": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "689": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 13, 10.89/4.15 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T74", 10.89/4.15 "T75" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "569": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 1, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T46", 10.89/4.15 "T47" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "602": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "603": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "604": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 11, 10.89/4.15 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T60", 10.89/4.15 "T61" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "725": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "605": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 11, 10.89/4.15 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T60", 10.89/4.15 "T61" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "726": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 14, 10.89/4.15 "term": "(log2 T83 (s T82) T81)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T81", 10.89/4.15 "T82", 10.89/4.15 "T83" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "606": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "607": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "608": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "729": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "609": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(',' (half (s (s T66)) X183) (log2 X183 (s (s (s (s (s (s (0))))))) T67))" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T66", 10.89/4.15 "T67" 10.89/4.15 ], 10.89/4.15 "free": ["X183"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "290": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 4, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X32"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "170": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 2, 10.89/4.15 "term": "(log2 T10 (0) T9)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": ["T9"], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "291": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X32"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "292": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 3, 10.89/4.15 "term": "(half (s (s T17)) X32)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X32"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "294": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "570": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 3, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T46", 10.89/4.15 "T47" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "571": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "692": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": -1, 10.89/4.15 "scope": -1, 10.89/4.15 "term": "(true)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "572": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "298": { 10.89/4.15 "goal": [ 10.89/4.15 { 10.89/4.15 "clause": 4, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 5, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }, 10.89/4.15 { 10.89/4.15 "clause": 6, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 } 10.89/4.15 ], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "573": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "694": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "299": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 4, 10.89/4.15 "scope": 4, 10.89/4.15 "term": "(half T23 X41)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [], 10.89/4.15 "free": ["X41"], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "574": { 10.89/4.15 "goal": [{ 10.89/4.15 "clause": 2, 10.89/4.15 "scope": 9, 10.89/4.15 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.15 }], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.15 "arithmetic": { 10.89/4.15 "type": "PlainIntegerRelationState", 10.89/4.15 "relations": [] 10.89/4.15 }, 10.89/4.15 "ground": [ 10.89/4.15 "T46", 10.89/4.15 "T47" 10.89/4.15 ], 10.89/4.15 "free": [], 10.89/4.15 "exprvars": [] 10.89/4.15 } 10.89/4.15 }, 10.89/4.15 "695": { 10.89/4.15 "goal": [], 10.89/4.15 "kb": { 10.89/4.15 "nonunifying": [], 10.89/4.15 "intvars": {}, 10.89/4.16 "arithmetic": { 10.89/4.16 "type": "PlainIntegerRelationState", 10.89/4.16 "relations": [] 10.89/4.16 }, 10.89/4.16 "ground": [], 10.89/4.16 "free": [], 10.89/4.16 "exprvars": [] 10.89/4.16 } 10.89/4.16 }, 10.89/4.16 "575": { 10.89/4.16 "goal": [{ 10.89/4.16 "clause": 3, 10.89/4.16 "scope": 9, 10.89/4.16 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.89/4.16 }], 10.89/4.16 "kb": { 10.89/4.16 "nonunifying": [], 10.89/4.16 "intvars": {}, 10.89/4.16 "arithmetic": { 10.89/4.16 "type": "PlainIntegerRelationState", 10.89/4.16 "relations": [] 10.89/4.16 }, 10.89/4.16 "ground": [ 10.89/4.16 "T46", 10.89/4.16 "T47" 10.89/4.16 ], 10.89/4.16 "free": [], 10.89/4.16 "exprvars": [] 10.89/4.16 } 10.89/4.16 }, 10.89/4.16 "576": { 10.89/4.16 "goal": [{ 10.89/4.16 "clause": -1, 10.89/4.16 "scope": -1, 10.89/4.16 "term": "(true)" 10.89/4.16 }], 10.89/4.16 "kb": { 10.89/4.16 "nonunifying": [], 10.89/4.16 "intvars": {}, 10.89/4.16 "arithmetic": { 10.89/4.16 "type": "PlainIntegerRelationState", 10.89/4.16 "relations": [] 10.89/4.16 }, 10.89/4.16 "ground": [], 10.89/4.16 "free": [], 10.89/4.16 "exprvars": [] 10.89/4.16 } 10.89/4.16 }, 10.89/4.16 "730": { 10.89/4.16 "goal": [], 10.89/4.16 "kb": { 10.89/4.16 "nonunifying": [], 10.89/4.16 "intvars": {}, 10.89/4.16 "arithmetic": { 10.89/4.16 "type": "PlainIntegerRelationState", 10.89/4.16 "relations": [] 10.89/4.16 }, 10.89/4.16 "ground": [], 10.89/4.16 "free": [], 10.89/4.16 "exprvars": [] 10.89/4.16 } 10.89/4.16 }, 10.89/4.16 "577": { 10.89/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "610": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "731": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "578": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "611": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(half (s (s T66)) X183)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T66"], 10.94/4.16 "free": ["X183"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "579": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(',' (half (s (s T52)) X137) (log2 X137 (s (s (s (s (0))))) T53))" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T52", 10.94/4.16 "T53" 10.94/4.16 ], 10.94/4.16 "free": ["X137"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "612": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T67", 10.94/4.16 "T68" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "613": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 1, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 3, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T67", 10.94/4.16 "T68" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "614": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 1, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T67", 10.94/4.16 "T68" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "735": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(',' (half (s (s T102)) X252) (log2 X252 (s (s T103)) T104))" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T102", 10.94/4.16 "T103", 10.94/4.16 "T104" 10.94/4.16 ], 10.94/4.16 "free": ["X252"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "615": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 3, 10.94/4.16 "scope": 12, 10.94/4.16 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T67", 10.94/4.16 "T68" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "616": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(true)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "737": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "617": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "618": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "580": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "581": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(half (s (s T52)) X137)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T52"], 10.94/4.16 "free": ["X137"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "582": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T53", 10.94/4.16 "T54" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "583": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 1, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 3, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T53", 10.94/4.16 "T54" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "100": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 1, 10.94/4.16 "scope": 2, 10.94/4.16 "term": "(log2 T10 (0) T9)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 2, 10.94/4.16 "term": "(log2 T10 (0) T9)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 3, 10.94/4.16 "scope": 2, 10.94/4.16 "term": "(log2 T10 (0) T9)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T9"], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "584": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 1, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T53", 10.94/4.16 "T54" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "585": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 3, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T53", 10.94/4.16 "T54" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "586": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(true)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "587": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "467": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(true)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "588": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "468": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "501": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "589": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 2, 10.94/4.16 "scope": 10, 10.94/4.16 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [ 10.94/4.16 "T53", 10.94/4.16 "T54" 10.94/4.16 ], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "469": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "502": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 4, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 5, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 6, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "503": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 4, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "504": { 10.94/4.16 "goal": [ 10.94/4.16 { 10.94/4.16 "clause": 5, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "clause": 6, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "505": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": -1, 10.94/4.16 "scope": -1, 10.94/4.16 "term": "(true)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "506": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "507": { 10.94/4.16 "goal": [], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": [], 10.94/4.16 "free": [], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "508": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 5, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "509": { 10.94/4.16 "goal": [{ 10.94/4.16 "clause": 6, 10.94/4.16 "scope": 7, 10.94/4.16 "term": "(half T37 X82)" 10.94/4.16 }], 10.94/4.16 "kb": { 10.94/4.16 "nonunifying": [], 10.94/4.16 "intvars": {}, 10.94/4.16 "arithmetic": { 10.94/4.16 "type": "PlainIntegerRelationState", 10.94/4.16 "relations": [] 10.94/4.16 }, 10.94/4.16 "ground": ["T37"], 10.94/4.16 "free": ["X82"], 10.94/4.16 "exprvars": [] 10.94/4.16 } 10.94/4.16 } 10.94/4.16 }, 10.94/4.16 "edges": [ 10.94/4.16 { 10.94/4.16 "from": 22, 10.94/4.16 "to": 23, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 23, 10.94/4.16 "to": 97, 10.94/4.16 "label": "ONLY EVAL with clause\nlog2(X8, X9) :- log2(X8, 0, X9).\nand substitutionT1 -> T10,\nX8 -> T10,\nT2 -> T9,\nX9 -> T9,\nT8 -> T10" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 97, 10.94/4.16 "to": 100, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 100, 10.94/4.16 "to": 124, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 100, 10.94/4.16 "to": 129, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 124, 10.94/4.16 "to": 158, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X16, X16).\nand substitutionT10 -> 0,\nX16 -> 0,\nT9 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 124, 10.94/4.16 "to": 162, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 129, 10.94/4.16 "to": 169, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 129, 10.94/4.16 "to": 170, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 158, 10.94/4.16 "to": 163, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 169, 10.94/4.16 "to": 240, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X21, X21).\nand substitutionT10 -> s(0),\nX21 -> 0,\nT9 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 169, 10.94/4.16 "to": 241, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 170, 10.94/4.16 "to": 245, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X29)), X30, X31) :- ','(half(s(s(X29)), X32), log2(X32, s(X30), X31)).\nand substitutionX29 -> T17,\nT10 -> s(s(T17)),\nX30 -> 0,\nT9 -> T16,\nX31 -> T16,\nT15 -> T17" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 170, 10.94/4.16 "to": 246, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 240, 10.94/4.16 "to": 242, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 245, 10.94/4.16 "to": 247, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 245, 10.94/4.16 "to": 248, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT17 is ground\nT18 is ground\nreplacements:X32 -> T18" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 247, 10.94/4.16 "to": 290, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 248, 10.94/4.16 "to": 323, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 290, 10.94/4.16 "to": 291, 10.94/4.16 "label": "BACKTRACK\nfor clause: half(0, 0)because of non-unification" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 291, 10.94/4.16 "to": 292, 10.94/4.16 "label": "BACKTRACK\nfor clause: half(s(0), 0)because of non-unification" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 292, 10.94/4.16 "to": 294, 10.94/4.16 "label": "ONLY EVAL with clause\nhalf(s(s(X39)), s(X40)) :- half(X39, X40).\nand substitutionT17 -> T23,\nX39 -> T23,\nX40 -> X41,\nX32 -> s(X41),\nT22 -> T23" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 294, 10.94/4.16 "to": 298, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 298, 10.94/4.16 "to": 299, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 298, 10.94/4.16 "to": 300, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 299, 10.94/4.16 "to": 304, 10.94/4.16 "label": "EVAL with clause\nhalf(0, 0).\nand substitutionT23 -> 0,\nX41 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 299, 10.94/4.16 "to": 305, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 300, 10.94/4.16 "to": 309, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 300, 10.94/4.16 "to": 310, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 304, 10.94/4.16 "to": 306, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 309, 10.94/4.16 "to": 313, 10.94/4.16 "label": "EVAL with clause\nhalf(s(0), 0).\nand substitutionT23 -> s(0),\nX41 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 309, 10.94/4.16 "to": 315, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 310, 10.94/4.16 "to": 319, 10.94/4.16 "label": "EVAL with clause\nhalf(s(s(X48)), s(X49)) :- half(X48, X49).\nand substitutionX48 -> T27,\nT23 -> s(s(T27)),\nX49 -> X50,\nX41 -> s(X50),\nT26 -> T27" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 310, 10.94/4.16 "to": 320, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 313, 10.94/4.16 "to": 316, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 319, 10.94/4.16 "to": 294, 10.94/4.16 "label": "INSTANCE with matching:\nT23 -> T27\nX41 -> X50" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 323, 10.94/4.16 "to": 388, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 323, 10.94/4.16 "to": 389, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 388, 10.94/4.16 "to": 467, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X57, X57).\nand substitutionT18 -> 0,\nX57 -> s(0),\nT16 -> s(0)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 388, 10.94/4.16 "to": 468, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 389, 10.94/4.16 "to": 470, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 389, 10.94/4.16 "to": 471, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 467, 10.94/4.16 "to": 469, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 470, 10.94/4.16 "to": 475, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X62, X62).\nand substitutionT18 -> s(0),\nX62 -> s(0),\nT16 -> s(0)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 470, 10.94/4.16 "to": 476, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 471, 10.94/4.16 "to": 481, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X70)), X71, X72) :- ','(half(s(s(X70)), X73), log2(X73, s(X71), X72)).\nand substitutionX70 -> T32,\nT18 -> s(s(T32)),\nX71 -> s(0),\nT16 -> T33,\nX72 -> T33" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 471, 10.94/4.16 "to": 482, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 475, 10.94/4.16 "to": 477, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 481, 10.94/4.16 "to": 486, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 481, 10.94/4.16 "to": 487, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT32 is ground\nT34 is ground\nreplacements:X73 -> T34" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 486, 10.94/4.16 "to": 493, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 487, 10.94/4.16 "to": 526, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 493, 10.94/4.16 "to": 495, 10.94/4.16 "label": "BACKTRACK\nfor clause: half(0, 0)because of non-unification" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 495, 10.94/4.16 "to": 497, 10.94/4.16 "label": "BACKTRACK\nfor clause: half(s(0), 0)because of non-unification" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 497, 10.94/4.16 "to": 501, 10.94/4.16 "label": "ONLY EVAL with clause\nhalf(s(s(X80)), s(X81)) :- half(X80, X81).\nand substitutionT32 -> T37,\nX80 -> T37,\nX81 -> X82,\nX73 -> s(X82)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 501, 10.94/4.16 "to": 502, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 502, 10.94/4.16 "to": 503, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 502, 10.94/4.16 "to": 504, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 503, 10.94/4.16 "to": 505, 10.94/4.16 "label": "EVAL with clause\nhalf(0, 0).\nand substitutionT37 -> 0,\nX82 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 503, 10.94/4.16 "to": 506, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 504, 10.94/4.16 "to": 508, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 504, 10.94/4.16 "to": 509, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 505, 10.94/4.16 "to": 507, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 508, 10.94/4.16 "to": 511, 10.94/4.16 "label": "EVAL with clause\nhalf(s(0), 0).\nand substitutionT37 -> s(0),\nX82 -> 0" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 508, 10.94/4.16 "to": 512, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 509, 10.94/4.16 "to": 519, 10.94/4.16 "label": "EVAL with clause\nhalf(s(s(X89)), s(X90)) :- half(X89, X90).\nand substitutionX89 -> T40,\nT37 -> s(s(T40)),\nX90 -> X91,\nX82 -> s(X91)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 509, 10.94/4.16 "to": 520, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 511, 10.94/4.16 "to": 514, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 519, 10.94/4.16 "to": 501, 10.94/4.16 "label": "INSTANCE with matching:\nT37 -> T40\nX82 -> X91" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 526, 10.94/4.16 "to": 527, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 526, 10.94/4.16 "to": 528, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 527, 10.94/4.16 "to": 531, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X98, X98).\nand substitutionT34 -> 0,\nX98 -> s(s(0)),\nT33 -> s(s(0))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 527, 10.94/4.16 "to": 532, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 528, 10.94/4.16 "to": 534, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 528, 10.94/4.16 "to": 535, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 531, 10.94/4.16 "to": 533, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 534, 10.94/4.16 "to": 538, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X103, X103).\nand substitutionT34 -> s(0),\nX103 -> s(s(0)),\nT33 -> s(s(0))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 534, 10.94/4.16 "to": 539, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 535, 10.94/4.16 "to": 541, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X111)), X112, X113) :- ','(half(s(s(X111)), X114), log2(X114, s(X112), X113)).\nand substitutionX111 -> T45,\nT34 -> s(s(T45)),\nX112 -> s(s(0)),\nT33 -> T46,\nX113 -> T46" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 535, 10.94/4.16 "to": 543, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 538, 10.94/4.16 "to": 540, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 541, 10.94/4.16 "to": 566, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 541, 10.94/4.16 "to": 567, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT45 is ground\nT47 is ground\nreplacements:X114 -> T47" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 566, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T45\nX73 -> X114" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 567, 10.94/4.16 "to": 568, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 568, 10.94/4.16 "to": 569, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 568, 10.94/4.16 "to": 570, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 569, 10.94/4.16 "to": 571, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X121, X121).\nand substitutionT47 -> 0,\nX121 -> s(s(s(0))),\nT46 -> s(s(s(0)))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 569, 10.94/4.16 "to": 572, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 570, 10.94/4.16 "to": 574, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 570, 10.94/4.16 "to": 575, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 571, 10.94/4.16 "to": 573, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 574, 10.94/4.16 "to": 576, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X126, X126).\nand substitutionT47 -> s(0),\nX126 -> s(s(s(0))),\nT46 -> s(s(s(0)))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 574, 10.94/4.16 "to": 577, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 575, 10.94/4.16 "to": 579, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X134)), X135, X136) :- ','(half(s(s(X134)), X137), log2(X137, s(X135), X136)).\nand substitutionX134 -> T52,\nT47 -> s(s(T52)),\nX135 -> s(s(s(0))),\nT46 -> T53,\nX136 -> T53" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 575, 10.94/4.16 "to": 580, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 576, 10.94/4.16 "to": 578, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 579, 10.94/4.16 "to": 581, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 579, 10.94/4.16 "to": 582, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT52 is ground\nT54 is ground\nreplacements:X137 -> T54" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 581, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T52\nX73 -> X137" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 582, 10.94/4.16 "to": 583, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 583, 10.94/4.16 "to": 584, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 583, 10.94/4.16 "to": 585, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 584, 10.94/4.16 "to": 586, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X144, X144).\nand substitutionT54 -> 0,\nX144 -> s(s(s(s(0)))),\nT53 -> s(s(s(s(0))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 584, 10.94/4.16 "to": 587, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 585, 10.94/4.16 "to": 589, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 585, 10.94/4.16 "to": 590, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 586, 10.94/4.16 "to": 588, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 589, 10.94/4.16 "to": 591, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X149, X149).\nand substitutionT54 -> s(0),\nX149 -> s(s(s(s(0)))),\nT53 -> s(s(s(s(0))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 589, 10.94/4.16 "to": 592, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 590, 10.94/4.16 "to": 594, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X157)), X158, X159) :- ','(half(s(s(X157)), X160), log2(X160, s(X158), X159)).\nand substitutionX157 -> T59,\nT54 -> s(s(T59)),\nX158 -> s(s(s(s(0)))),\nT53 -> T60,\nX159 -> T60" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 590, 10.94/4.16 "to": 595, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 591, 10.94/4.16 "to": 593, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 594, 10.94/4.16 "to": 596, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 594, 10.94/4.16 "to": 597, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT59 is ground\nT61 is ground\nreplacements:X160 -> T61" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 596, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T59\nX73 -> X160" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 597, 10.94/4.16 "to": 598, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 598, 10.94/4.16 "to": 599, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 598, 10.94/4.16 "to": 600, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 599, 10.94/4.16 "to": 601, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X167, X167).\nand substitutionT61 -> 0,\nX167 -> s(s(s(s(s(0))))),\nT60 -> s(s(s(s(s(0)))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 599, 10.94/4.16 "to": 602, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 600, 10.94/4.16 "to": 604, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 600, 10.94/4.16 "to": 605, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 601, 10.94/4.16 "to": 603, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 604, 10.94/4.16 "to": 606, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X172, X172).\nand substitutionT61 -> s(0),\nX172 -> s(s(s(s(s(0))))),\nT60 -> s(s(s(s(s(0)))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 604, 10.94/4.16 "to": 607, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 605, 10.94/4.16 "to": 609, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X180)), X181, X182) :- ','(half(s(s(X180)), X183), log2(X183, s(X181), X182)).\nand substitutionX180 -> T66,\nT61 -> s(s(T66)),\nX181 -> s(s(s(s(s(0))))),\nT60 -> T67,\nX182 -> T67" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 605, 10.94/4.16 "to": 610, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 606, 10.94/4.16 "to": 608, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 609, 10.94/4.16 "to": 611, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 609, 10.94/4.16 "to": 612, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT66 is ground\nT68 is ground\nreplacements:X183 -> T68" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 611, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T66\nX73 -> X183" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 612, 10.94/4.16 "to": 613, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 613, 10.94/4.16 "to": 614, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 613, 10.94/4.16 "to": 615, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 614, 10.94/4.16 "to": 616, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X190, X190).\nand substitutionT68 -> 0,\nX190 -> s(s(s(s(s(s(0)))))),\nT67 -> s(s(s(s(s(s(0))))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 614, 10.94/4.16 "to": 617, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 615, 10.94/4.16 "to": 632, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 615, 10.94/4.16 "to": 635, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 616, 10.94/4.16 "to": 618, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 632, 10.94/4.16 "to": 654, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X195, X195).\nand substitutionT68 -> s(0),\nX195 -> s(s(s(s(s(s(0)))))),\nT67 -> s(s(s(s(s(s(0))))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 632, 10.94/4.16 "to": 655, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 635, 10.94/4.16 "to": 657, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X203)), X204, X205) :- ','(half(s(s(X203)), X206), log2(X206, s(X204), X205)).\nand substitutionX203 -> T73,\nT68 -> s(s(T73)),\nX204 -> s(s(s(s(s(s(0)))))),\nT67 -> T74,\nX205 -> T74" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 635, 10.94/4.16 "to": 658, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 654, 10.94/4.16 "to": 656, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 657, 10.94/4.16 "to": 673, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 657, 10.94/4.16 "to": 674, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT73 is ground\nT75 is ground\nreplacements:X206 -> T75" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 673, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T73\nX73 -> X206" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 674, 10.94/4.16 "to": 678, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 678, 10.94/4.16 "to": 681, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 678, 10.94/4.16 "to": 682, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 681, 10.94/4.16 "to": 683, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X213, X213).\nand substitutionT75 -> 0,\nX213 -> s(s(s(s(s(s(s(0))))))),\nT74 -> s(s(s(s(s(s(s(0)))))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 681, 10.94/4.16 "to": 684, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 682, 10.94/4.16 "to": 688, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 682, 10.94/4.16 "to": 689, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 683, 10.94/4.16 "to": 685, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 688, 10.94/4.16 "to": 692, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X218, X218).\nand substitutionT75 -> s(0),\nX218 -> s(s(s(s(s(s(s(0))))))),\nT74 -> s(s(s(s(s(s(s(0)))))))" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 688, 10.94/4.16 "to": 694, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 689, 10.94/4.16 "to": 701, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X226)), X227, X228) :- ','(half(s(s(X226)), X229), log2(X229, s(X227), X228)).\nand substitutionX226 -> T80,\nT75 -> s(s(T80)),\nX227 -> s(s(s(s(s(s(s(0))))))),\nT74 -> T81,\nX228 -> T81" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 689, 10.94/4.16 "to": 702, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 692, 10.94/4.16 "to": 695, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 701, 10.94/4.16 "to": 706, 10.94/4.16 "label": "GENERALIZATION\nT82 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT82 is ground" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 706, 10.94/4.16 "to": 709, 10.94/4.16 "label": "SPLIT 1" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 706, 10.94/4.16 "to": 711, 10.94/4.16 "label": "SPLIT 2\nnew knowledge:\nT80 is ground\nT83 is ground\nreplacements:X229 -> T83" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 709, 10.94/4.16 "to": 486, 10.94/4.16 "label": "INSTANCE with matching:\nT32 -> T80\nX73 -> X229" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 711, 10.94/4.16 "to": 713, 10.94/4.16 "label": "CASE" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 713, 10.94/4.16 "to": 714, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 713, 10.94/4.16 "to": 715, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 714, 10.94/4.16 "to": 719, 10.94/4.16 "label": "EVAL with clause\nlog2(0, X236, X236).\nand substitutionT83 -> 0,\nT82 -> T90,\nX236 -> s(T90),\nT81 -> s(T90)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 714, 10.94/4.16 "to": 720, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 715, 10.94/4.16 "to": 725, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 715, 10.94/4.16 "to": 726, 10.94/4.16 "label": "PARALLEL" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 719, 10.94/4.16 "to": 721, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 725, 10.94/4.16 "to": 729, 10.94/4.16 "label": "EVAL with clause\nlog2(s(0), X241, X241).\nand substitutionT83 -> s(0),\nT82 -> T95,\nX241 -> s(T95),\nT81 -> s(T95)" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 725, 10.94/4.16 "to": 730, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 726, 10.94/4.16 "to": 735, 10.94/4.16 "label": "EVAL with clause\nlog2(s(s(X249)), X250, X251) :- ','(half(s(s(X249)), X252), log2(X252, s(X250), X251)).\nand substitutionX249 -> T102,\nT83 -> s(s(T102)),\nT82 -> T103,\nX250 -> s(T103),\nT81 -> T104,\nX251 -> T104" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 726, 10.94/4.16 "to": 737, 10.94/4.16 "label": "EVAL-BACKTRACK" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 729, 10.94/4.16 "to": 731, 10.94/4.16 "label": "SUCCESS" 10.94/4.16 }, 10.94/4.16 { 10.94/4.16 "from": 735, 10.94/4.16 "to": 706, 10.94/4.16 "label": "INSTANCE with matching:\nT80 -> T102\nX229 -> X252\nT82 -> s(T103)\nT81 -> T104" 10.94/4.16 } 10.94/4.16 ], 10.94/4.16 "type": "Graph" 10.94/4.16 } 10.94/4.16 } 10.94/4.16 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (89) 10.94/4.16 Obligation: 10.94/4.16 Q restricted rewrite system: 10.94/4.16 The TRS R consists of the following rules: 10.94/4.16 10.94/4.16 f22_in(0) -> f22_out1(0) 10.94/4.16 f22_in(0) -> f22_out1(s(0)) 10.94/4.16 f22_in(T16) -> U1(f245_in(T16), T16) 10.94/4.16 U1(f245_out1(T17, X32), T16) -> f22_out1(s(s(T17))) 10.94/4.16 f294_in -> f294_out1(0, 0) 10.94/4.16 f294_in -> f294_out1(s(0), 0) 10.94/4.16 f294_in -> U2(f294_in) 10.94/4.16 U2(f294_out1(T27, X50)) -> f294_out1(s(s(T27)), s(X50)) 10.94/4.16 f501_in(0) -> f501_out1(0) 10.94/4.16 f501_in(s(0)) -> f501_out1(0) 10.94/4.16 f501_in(s(s(T40))) -> U3(f501_in(T40), s(s(T40))) 10.94/4.16 U3(f501_out1(X91), s(s(T40))) -> f501_out1(s(X91)) 10.94/4.16 f486_in(T37) -> U4(f501_in(T37), T37) 10.94/4.16 U4(f501_out1(X82), T37) -> f486_out1(s(X82)) 10.94/4.16 f247_in -> U5(f294_in) 10.94/4.16 U5(f294_out1(T23, X41)) -> f247_out1(T23, s(X41)) 10.94/4.16 f248_in(0, s(0)) -> f248_out1 10.94/4.16 f248_in(s(0), s(0)) -> f248_out1 10.94/4.16 f248_in(s(s(T32)), T33) -> U6(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.16 U6(f481_out1(X73), s(s(T32)), T33) -> f248_out1 10.94/4.16 f487_in(0, s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(0), s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(s(T45)), T46) -> U7(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.16 U7(f541_out1(X114), s(s(T45)), T46) -> f487_out1 10.94/4.16 f567_in(0, s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(0), s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(s(T52)), T53) -> U8(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.16 U8(f579_out1(X137), s(s(T52)), T53) -> f567_out1 10.94/4.16 f582_in(0, s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(0), s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(s(T59)), T60) -> U9(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.16 U9(f594_out1(X160), s(s(T59)), T60) -> f582_out1 10.94/4.16 f597_in(0, s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(0), s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(s(T66)), T67) -> U10(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.16 U10(f609_out1(X183), s(s(T66)), T67) -> f597_out1 10.94/4.16 f612_in(0, s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(0), s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(s(T73)), T74) -> U11(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.16 U11(f657_out1(X206), s(s(T73)), T74) -> f612_out1 10.94/4.16 f674_in(0, s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(s(T80)), T81) -> U12(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.16 U12(f706_out1(X229), s(s(T80)), T81) -> f674_out1 10.94/4.16 f711_in(0, T90, s(T90)) -> f711_out1 10.94/4.16 f711_in(s(0), T95, s(T95)) -> f711_out1 10.94/4.16 f711_in(s(s(T102)), T103, T104) -> U13(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.16 U13(f706_out1(X252), s(s(T102)), T103, T104) -> f711_out1 10.94/4.16 f245_in(T16) -> U14(f247_in, T16) 10.94/4.16 U14(f247_out1(T17, T18), T16) -> U15(f248_in(T18, T16), T16, T17, T18) 10.94/4.16 U15(f248_out1, T16, T17, T18) -> f245_out1(T17, T18) 10.94/4.16 f481_in(T32, T33) -> U16(f486_in(T32), T32, T33) 10.94/4.16 U16(f486_out1(T34), T32, T33) -> U17(f487_in(T34, T33), T32, T33, T34) 10.94/4.16 U17(f487_out1, T32, T33, T34) -> f481_out1(T34) 10.94/4.16 f541_in(T45, T46) -> U18(f486_in(T45), T45, T46) 10.94/4.16 U18(f486_out1(T47), T45, T46) -> U19(f567_in(T47, T46), T45, T46, T47) 10.94/4.16 U19(f567_out1, T45, T46, T47) -> f541_out1(T47) 10.94/4.16 f579_in(T52, T53) -> U20(f486_in(T52), T52, T53) 10.94/4.16 U20(f486_out1(T54), T52, T53) -> U21(f582_in(T54, T53), T52, T53, T54) 10.94/4.16 U21(f582_out1, T52, T53, T54) -> f579_out1(T54) 10.94/4.16 f594_in(T59, T60) -> U22(f486_in(T59), T59, T60) 10.94/4.16 U22(f486_out1(T61), T59, T60) -> U23(f597_in(T61, T60), T59, T60, T61) 10.94/4.16 U23(f597_out1, T59, T60, T61) -> f594_out1(T61) 10.94/4.16 f609_in(T66, T67) -> U24(f486_in(T66), T66, T67) 10.94/4.16 U24(f486_out1(T68), T66, T67) -> U25(f612_in(T68, T67), T66, T67, T68) 10.94/4.16 U25(f612_out1, T66, T67, T68) -> f609_out1(T68) 10.94/4.16 f657_in(T73, T74) -> U26(f486_in(T73), T73, T74) 10.94/4.16 U26(f486_out1(T75), T73, T74) -> U27(f674_in(T75, T74), T73, T74, T75) 10.94/4.16 U27(f674_out1, T73, T74, T75) -> f657_out1(T75) 10.94/4.16 f706_in(T80, T82, T81) -> U28(f486_in(T80), T80, T82, T81) 10.94/4.16 U28(f486_out1(T83), T80, T82, T81) -> U29(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.16 U29(f711_out1, T80, T82, T81, T83) -> f706_out1(T83) 10.94/4.16 10.94/4.16 Q is empty. 10.94/4.16 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (90) DependencyPairsProof (EQUIVALENT) 10.94/4.16 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (91) 10.94/4.16 Obligation: 10.94/4.16 Q DP problem: 10.94/4.16 The TRS P consists of the following rules: 10.94/4.16 10.94/4.16 F22_IN(T16) -> U1^1(f245_in(T16), T16) 10.94/4.16 F22_IN(T16) -> F245_IN(T16) 10.94/4.16 F294_IN -> U2^1(f294_in) 10.94/4.16 F294_IN -> F294_IN 10.94/4.16 F501_IN(s(s(T40))) -> U3^1(f501_in(T40), s(s(T40))) 10.94/4.16 F501_IN(s(s(T40))) -> F501_IN(T40) 10.94/4.16 F486_IN(T37) -> U4^1(f501_in(T37), T37) 10.94/4.16 F486_IN(T37) -> F501_IN(T37) 10.94/4.16 F247_IN -> U5^1(f294_in) 10.94/4.16 F247_IN -> F294_IN 10.94/4.16 F248_IN(s(s(T32)), T33) -> U6^1(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.16 F248_IN(s(s(T32)), T33) -> F481_IN(T32, T33) 10.94/4.16 F487_IN(s(s(T45)), T46) -> U7^1(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.16 F487_IN(s(s(T45)), T46) -> F541_IN(T45, T46) 10.94/4.16 F567_IN(s(s(T52)), T53) -> U8^1(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.16 F567_IN(s(s(T52)), T53) -> F579_IN(T52, T53) 10.94/4.16 F582_IN(s(s(T59)), T60) -> U9^1(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.16 F582_IN(s(s(T59)), T60) -> F594_IN(T59, T60) 10.94/4.16 F597_IN(s(s(T66)), T67) -> U10^1(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.16 F597_IN(s(s(T66)), T67) -> F609_IN(T66, T67) 10.94/4.16 F612_IN(s(s(T73)), T74) -> U11^1(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.16 F612_IN(s(s(T73)), T74) -> F657_IN(T73, T74) 10.94/4.16 F674_IN(s(s(T80)), T81) -> U12^1(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.16 F674_IN(s(s(T80)), T81) -> F706_IN(T80, s(s(s(s(s(s(s(0))))))), T81) 10.94/4.16 F711_IN(s(s(T102)), T103, T104) -> U13^1(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.16 F711_IN(s(s(T102)), T103, T104) -> F706_IN(T102, s(T103), T104) 10.94/4.16 F245_IN(T16) -> U14^1(f247_in, T16) 10.94/4.16 F245_IN(T16) -> F247_IN 10.94/4.16 U14^1(f247_out1(T17, T18), T16) -> U15^1(f248_in(T18, T16), T16, T17, T18) 10.94/4.16 U14^1(f247_out1(T17, T18), T16) -> F248_IN(T18, T16) 10.94/4.16 F481_IN(T32, T33) -> U16^1(f486_in(T32), T32, T33) 10.94/4.16 F481_IN(T32, T33) -> F486_IN(T32) 10.94/4.16 U16^1(f486_out1(T34), T32, T33) -> U17^1(f487_in(T34, T33), T32, T33, T34) 10.94/4.16 U16^1(f486_out1(T34), T32, T33) -> F487_IN(T34, T33) 10.94/4.16 F541_IN(T45, T46) -> U18^1(f486_in(T45), T45, T46) 10.94/4.16 F541_IN(T45, T46) -> F486_IN(T45) 10.94/4.16 U18^1(f486_out1(T47), T45, T46) -> U19^1(f567_in(T47, T46), T45, T46, T47) 10.94/4.16 U18^1(f486_out1(T47), T45, T46) -> F567_IN(T47, T46) 10.94/4.16 F579_IN(T52, T53) -> U20^1(f486_in(T52), T52, T53) 10.94/4.16 F579_IN(T52, T53) -> F486_IN(T52) 10.94/4.16 U20^1(f486_out1(T54), T52, T53) -> U21^1(f582_in(T54, T53), T52, T53, T54) 10.94/4.16 U20^1(f486_out1(T54), T52, T53) -> F582_IN(T54, T53) 10.94/4.16 F594_IN(T59, T60) -> U22^1(f486_in(T59), T59, T60) 10.94/4.16 F594_IN(T59, T60) -> F486_IN(T59) 10.94/4.16 U22^1(f486_out1(T61), T59, T60) -> U23^1(f597_in(T61, T60), T59, T60, T61) 10.94/4.16 U22^1(f486_out1(T61), T59, T60) -> F597_IN(T61, T60) 10.94/4.16 F609_IN(T66, T67) -> U24^1(f486_in(T66), T66, T67) 10.94/4.16 F609_IN(T66, T67) -> F486_IN(T66) 10.94/4.16 U24^1(f486_out1(T68), T66, T67) -> U25^1(f612_in(T68, T67), T66, T67, T68) 10.94/4.16 U24^1(f486_out1(T68), T66, T67) -> F612_IN(T68, T67) 10.94/4.16 F657_IN(T73, T74) -> U26^1(f486_in(T73), T73, T74) 10.94/4.16 F657_IN(T73, T74) -> F486_IN(T73) 10.94/4.16 U26^1(f486_out1(T75), T73, T74) -> U27^1(f674_in(T75, T74), T73, T74, T75) 10.94/4.16 U26^1(f486_out1(T75), T73, T74) -> F674_IN(T75, T74) 10.94/4.16 F706_IN(T80, T82, T81) -> U28^1(f486_in(T80), T80, T82, T81) 10.94/4.16 F706_IN(T80, T82, T81) -> F486_IN(T80) 10.94/4.16 U28^1(f486_out1(T83), T80, T82, T81) -> U29^1(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.16 U28^1(f486_out1(T83), T80, T82, T81) -> F711_IN(T83, T82, T81) 10.94/4.16 10.94/4.16 The TRS R consists of the following rules: 10.94/4.16 10.94/4.16 f22_in(0) -> f22_out1(0) 10.94/4.16 f22_in(0) -> f22_out1(s(0)) 10.94/4.16 f22_in(T16) -> U1(f245_in(T16), T16) 10.94/4.16 U1(f245_out1(T17, X32), T16) -> f22_out1(s(s(T17))) 10.94/4.16 f294_in -> f294_out1(0, 0) 10.94/4.16 f294_in -> f294_out1(s(0), 0) 10.94/4.16 f294_in -> U2(f294_in) 10.94/4.16 U2(f294_out1(T27, X50)) -> f294_out1(s(s(T27)), s(X50)) 10.94/4.16 f501_in(0) -> f501_out1(0) 10.94/4.16 f501_in(s(0)) -> f501_out1(0) 10.94/4.16 f501_in(s(s(T40))) -> U3(f501_in(T40), s(s(T40))) 10.94/4.16 U3(f501_out1(X91), s(s(T40))) -> f501_out1(s(X91)) 10.94/4.16 f486_in(T37) -> U4(f501_in(T37), T37) 10.94/4.16 U4(f501_out1(X82), T37) -> f486_out1(s(X82)) 10.94/4.16 f247_in -> U5(f294_in) 10.94/4.16 U5(f294_out1(T23, X41)) -> f247_out1(T23, s(X41)) 10.94/4.16 f248_in(0, s(0)) -> f248_out1 10.94/4.16 f248_in(s(0), s(0)) -> f248_out1 10.94/4.16 f248_in(s(s(T32)), T33) -> U6(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.16 U6(f481_out1(X73), s(s(T32)), T33) -> f248_out1 10.94/4.16 f487_in(0, s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(0), s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(s(T45)), T46) -> U7(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.16 U7(f541_out1(X114), s(s(T45)), T46) -> f487_out1 10.94/4.16 f567_in(0, s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(0), s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(s(T52)), T53) -> U8(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.16 U8(f579_out1(X137), s(s(T52)), T53) -> f567_out1 10.94/4.16 f582_in(0, s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(0), s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(s(T59)), T60) -> U9(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.16 U9(f594_out1(X160), s(s(T59)), T60) -> f582_out1 10.94/4.16 f597_in(0, s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(0), s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(s(T66)), T67) -> U10(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.16 U10(f609_out1(X183), s(s(T66)), T67) -> f597_out1 10.94/4.16 f612_in(0, s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(0), s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(s(T73)), T74) -> U11(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.16 U11(f657_out1(X206), s(s(T73)), T74) -> f612_out1 10.94/4.16 f674_in(0, s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(s(T80)), T81) -> U12(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.16 U12(f706_out1(X229), s(s(T80)), T81) -> f674_out1 10.94/4.16 f711_in(0, T90, s(T90)) -> f711_out1 10.94/4.16 f711_in(s(0), T95, s(T95)) -> f711_out1 10.94/4.16 f711_in(s(s(T102)), T103, T104) -> U13(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.16 U13(f706_out1(X252), s(s(T102)), T103, T104) -> f711_out1 10.94/4.16 f245_in(T16) -> U14(f247_in, T16) 10.94/4.16 U14(f247_out1(T17, T18), T16) -> U15(f248_in(T18, T16), T16, T17, T18) 10.94/4.16 U15(f248_out1, T16, T17, T18) -> f245_out1(T17, T18) 10.94/4.16 f481_in(T32, T33) -> U16(f486_in(T32), T32, T33) 10.94/4.16 U16(f486_out1(T34), T32, T33) -> U17(f487_in(T34, T33), T32, T33, T34) 10.94/4.16 U17(f487_out1, T32, T33, T34) -> f481_out1(T34) 10.94/4.16 f541_in(T45, T46) -> U18(f486_in(T45), T45, T46) 10.94/4.16 U18(f486_out1(T47), T45, T46) -> U19(f567_in(T47, T46), T45, T46, T47) 10.94/4.16 U19(f567_out1, T45, T46, T47) -> f541_out1(T47) 10.94/4.16 f579_in(T52, T53) -> U20(f486_in(T52), T52, T53) 10.94/4.16 U20(f486_out1(T54), T52, T53) -> U21(f582_in(T54, T53), T52, T53, T54) 10.94/4.16 U21(f582_out1, T52, T53, T54) -> f579_out1(T54) 10.94/4.16 f594_in(T59, T60) -> U22(f486_in(T59), T59, T60) 10.94/4.16 U22(f486_out1(T61), T59, T60) -> U23(f597_in(T61, T60), T59, T60, T61) 10.94/4.16 U23(f597_out1, T59, T60, T61) -> f594_out1(T61) 10.94/4.16 f609_in(T66, T67) -> U24(f486_in(T66), T66, T67) 10.94/4.16 U24(f486_out1(T68), T66, T67) -> U25(f612_in(T68, T67), T66, T67, T68) 10.94/4.16 U25(f612_out1, T66, T67, T68) -> f609_out1(T68) 10.94/4.16 f657_in(T73, T74) -> U26(f486_in(T73), T73, T74) 10.94/4.16 U26(f486_out1(T75), T73, T74) -> U27(f674_in(T75, T74), T73, T74, T75) 10.94/4.16 U27(f674_out1, T73, T74, T75) -> f657_out1(T75) 10.94/4.16 f706_in(T80, T82, T81) -> U28(f486_in(T80), T80, T82, T81) 10.94/4.16 U28(f486_out1(T83), T80, T82, T81) -> U29(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.16 U29(f711_out1, T80, T82, T81, T83) -> f706_out1(T83) 10.94/4.16 10.94/4.16 Q is empty. 10.94/4.16 We have to consider all minimal (P,Q,R)-chains. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (92) DependencyGraphProof (EQUIVALENT) 10.94/4.16 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 53 less nodes. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (93) 10.94/4.16 Complex Obligation (AND) 10.94/4.16 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (94) 10.94/4.16 Obligation: 10.94/4.16 Q DP problem: 10.94/4.16 The TRS P consists of the following rules: 10.94/4.16 10.94/4.16 F501_IN(s(s(T40))) -> F501_IN(T40) 10.94/4.16 10.94/4.16 The TRS R consists of the following rules: 10.94/4.16 10.94/4.16 f22_in(0) -> f22_out1(0) 10.94/4.16 f22_in(0) -> f22_out1(s(0)) 10.94/4.16 f22_in(T16) -> U1(f245_in(T16), T16) 10.94/4.16 U1(f245_out1(T17, X32), T16) -> f22_out1(s(s(T17))) 10.94/4.16 f294_in -> f294_out1(0, 0) 10.94/4.16 f294_in -> f294_out1(s(0), 0) 10.94/4.16 f294_in -> U2(f294_in) 10.94/4.16 U2(f294_out1(T27, X50)) -> f294_out1(s(s(T27)), s(X50)) 10.94/4.16 f501_in(0) -> f501_out1(0) 10.94/4.16 f501_in(s(0)) -> f501_out1(0) 10.94/4.16 f501_in(s(s(T40))) -> U3(f501_in(T40), s(s(T40))) 10.94/4.16 U3(f501_out1(X91), s(s(T40))) -> f501_out1(s(X91)) 10.94/4.16 f486_in(T37) -> U4(f501_in(T37), T37) 10.94/4.16 U4(f501_out1(X82), T37) -> f486_out1(s(X82)) 10.94/4.16 f247_in -> U5(f294_in) 10.94/4.16 U5(f294_out1(T23, X41)) -> f247_out1(T23, s(X41)) 10.94/4.16 f248_in(0, s(0)) -> f248_out1 10.94/4.16 f248_in(s(0), s(0)) -> f248_out1 10.94/4.16 f248_in(s(s(T32)), T33) -> U6(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.16 U6(f481_out1(X73), s(s(T32)), T33) -> f248_out1 10.94/4.16 f487_in(0, s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(0), s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(s(T45)), T46) -> U7(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.16 U7(f541_out1(X114), s(s(T45)), T46) -> f487_out1 10.94/4.16 f567_in(0, s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(0), s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(s(T52)), T53) -> U8(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.16 U8(f579_out1(X137), s(s(T52)), T53) -> f567_out1 10.94/4.16 f582_in(0, s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(0), s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(s(T59)), T60) -> U9(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.16 U9(f594_out1(X160), s(s(T59)), T60) -> f582_out1 10.94/4.16 f597_in(0, s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(0), s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(s(T66)), T67) -> U10(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.16 U10(f609_out1(X183), s(s(T66)), T67) -> f597_out1 10.94/4.16 f612_in(0, s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(0), s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.16 f612_in(s(s(T73)), T74) -> U11(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.16 U11(f657_out1(X206), s(s(T73)), T74) -> f612_out1 10.94/4.16 f674_in(0, s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.16 f674_in(s(s(T80)), T81) -> U12(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.16 U12(f706_out1(X229), s(s(T80)), T81) -> f674_out1 10.94/4.16 f711_in(0, T90, s(T90)) -> f711_out1 10.94/4.16 f711_in(s(0), T95, s(T95)) -> f711_out1 10.94/4.16 f711_in(s(s(T102)), T103, T104) -> U13(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.16 U13(f706_out1(X252), s(s(T102)), T103, T104) -> f711_out1 10.94/4.16 f245_in(T16) -> U14(f247_in, T16) 10.94/4.16 U14(f247_out1(T17, T18), T16) -> U15(f248_in(T18, T16), T16, T17, T18) 10.94/4.16 U15(f248_out1, T16, T17, T18) -> f245_out1(T17, T18) 10.94/4.16 f481_in(T32, T33) -> U16(f486_in(T32), T32, T33) 10.94/4.16 U16(f486_out1(T34), T32, T33) -> U17(f487_in(T34, T33), T32, T33, T34) 10.94/4.16 U17(f487_out1, T32, T33, T34) -> f481_out1(T34) 10.94/4.16 f541_in(T45, T46) -> U18(f486_in(T45), T45, T46) 10.94/4.16 U18(f486_out1(T47), T45, T46) -> U19(f567_in(T47, T46), T45, T46, T47) 10.94/4.16 U19(f567_out1, T45, T46, T47) -> f541_out1(T47) 10.94/4.16 f579_in(T52, T53) -> U20(f486_in(T52), T52, T53) 10.94/4.16 U20(f486_out1(T54), T52, T53) -> U21(f582_in(T54, T53), T52, T53, T54) 10.94/4.16 U21(f582_out1, T52, T53, T54) -> f579_out1(T54) 10.94/4.16 f594_in(T59, T60) -> U22(f486_in(T59), T59, T60) 10.94/4.16 U22(f486_out1(T61), T59, T60) -> U23(f597_in(T61, T60), T59, T60, T61) 10.94/4.16 U23(f597_out1, T59, T60, T61) -> f594_out1(T61) 10.94/4.16 f609_in(T66, T67) -> U24(f486_in(T66), T66, T67) 10.94/4.16 U24(f486_out1(T68), T66, T67) -> U25(f612_in(T68, T67), T66, T67, T68) 10.94/4.16 U25(f612_out1, T66, T67, T68) -> f609_out1(T68) 10.94/4.16 f657_in(T73, T74) -> U26(f486_in(T73), T73, T74) 10.94/4.16 U26(f486_out1(T75), T73, T74) -> U27(f674_in(T75, T74), T73, T74, T75) 10.94/4.16 U27(f674_out1, T73, T74, T75) -> f657_out1(T75) 10.94/4.16 f706_in(T80, T82, T81) -> U28(f486_in(T80), T80, T82, T81) 10.94/4.16 U28(f486_out1(T83), T80, T82, T81) -> U29(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.16 U29(f711_out1, T80, T82, T81, T83) -> f706_out1(T83) 10.94/4.16 10.94/4.16 Q is empty. 10.94/4.16 We have to consider all minimal (P,Q,R)-chains. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (95) UsableRulesProof (EQUIVALENT) 10.94/4.16 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. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (96) 10.94/4.16 Obligation: 10.94/4.16 Q DP problem: 10.94/4.16 The TRS P consists of the following rules: 10.94/4.16 10.94/4.16 F501_IN(s(s(T40))) -> F501_IN(T40) 10.94/4.16 10.94/4.16 R is empty. 10.94/4.16 Q is empty. 10.94/4.16 We have to consider all minimal (P,Q,R)-chains. 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (97) QDPSizeChangeProof (EQUIVALENT) 10.94/4.16 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. 10.94/4.16 10.94/4.16 From the DPs we obtained the following set of size-change graphs: 10.94/4.16 *F501_IN(s(s(T40))) -> F501_IN(T40) 10.94/4.16 The graph contains the following edges 1 > 1 10.94/4.16 10.94/4.16 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (98) 10.94/4.16 YES 10.94/4.16 10.94/4.16 ---------------------------------------- 10.94/4.16 10.94/4.16 (99) 10.94/4.16 Obligation: 10.94/4.16 Q DP problem: 10.94/4.16 The TRS P consists of the following rules: 10.94/4.16 10.94/4.16 F706_IN(T80, T82, T81) -> U28^1(f486_in(T80), T80, T82, T81) 10.94/4.16 U28^1(f486_out1(T83), T80, T82, T81) -> F711_IN(T83, T82, T81) 10.94/4.16 F711_IN(s(s(T102)), T103, T104) -> F706_IN(T102, s(T103), T104) 10.94/4.16 10.94/4.16 The TRS R consists of the following rules: 10.94/4.16 10.94/4.16 f22_in(0) -> f22_out1(0) 10.94/4.16 f22_in(0) -> f22_out1(s(0)) 10.94/4.16 f22_in(T16) -> U1(f245_in(T16), T16) 10.94/4.16 U1(f245_out1(T17, X32), T16) -> f22_out1(s(s(T17))) 10.94/4.16 f294_in -> f294_out1(0, 0) 10.94/4.16 f294_in -> f294_out1(s(0), 0) 10.94/4.16 f294_in -> U2(f294_in) 10.94/4.16 U2(f294_out1(T27, X50)) -> f294_out1(s(s(T27)), s(X50)) 10.94/4.16 f501_in(0) -> f501_out1(0) 10.94/4.16 f501_in(s(0)) -> f501_out1(0) 10.94/4.16 f501_in(s(s(T40))) -> U3(f501_in(T40), s(s(T40))) 10.94/4.16 U3(f501_out1(X91), s(s(T40))) -> f501_out1(s(X91)) 10.94/4.16 f486_in(T37) -> U4(f501_in(T37), T37) 10.94/4.16 U4(f501_out1(X82), T37) -> f486_out1(s(X82)) 10.94/4.16 f247_in -> U5(f294_in) 10.94/4.16 U5(f294_out1(T23, X41)) -> f247_out1(T23, s(X41)) 10.94/4.16 f248_in(0, s(0)) -> f248_out1 10.94/4.16 f248_in(s(0), s(0)) -> f248_out1 10.94/4.16 f248_in(s(s(T32)), T33) -> U6(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.16 U6(f481_out1(X73), s(s(T32)), T33) -> f248_out1 10.94/4.16 f487_in(0, s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(0), s(s(0))) -> f487_out1 10.94/4.16 f487_in(s(s(T45)), T46) -> U7(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.16 U7(f541_out1(X114), s(s(T45)), T46) -> f487_out1 10.94/4.16 f567_in(0, s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(0), s(s(s(0)))) -> f567_out1 10.94/4.16 f567_in(s(s(T52)), T53) -> U8(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.16 U8(f579_out1(X137), s(s(T52)), T53) -> f567_out1 10.94/4.16 f582_in(0, s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(0), s(s(s(s(0))))) -> f582_out1 10.94/4.16 f582_in(s(s(T59)), T60) -> U9(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.16 U9(f594_out1(X160), s(s(T59)), T60) -> f582_out1 10.94/4.16 f597_in(0, s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(0), s(s(s(s(s(0)))))) -> f597_out1 10.94/4.16 f597_in(s(s(T66)), T67) -> U10(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.17 U10(f609_out1(X183), s(s(T66)), T67) -> f597_out1 10.94/4.17 f612_in(0, s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.17 f612_in(s(0), s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.17 f612_in(s(s(T73)), T74) -> U11(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.17 U11(f657_out1(X206), s(s(T73)), T74) -> f612_out1 10.94/4.17 f674_in(0, s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.17 f674_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.17 f674_in(s(s(T80)), T81) -> U12(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.17 U12(f706_out1(X229), s(s(T80)), T81) -> f674_out1 10.94/4.17 f711_in(0, T90, s(T90)) -> f711_out1 10.94/4.17 f711_in(s(0), T95, s(T95)) -> f711_out1 10.94/4.17 f711_in(s(s(T102)), T103, T104) -> U13(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.17 U13(f706_out1(X252), s(s(T102)), T103, T104) -> f711_out1 10.94/4.17 f245_in(T16) -> U14(f247_in, T16) 10.94/4.17 U14(f247_out1(T17, T18), T16) -> U15(f248_in(T18, T16), T16, T17, T18) 10.94/4.17 U15(f248_out1, T16, T17, T18) -> f245_out1(T17, T18) 10.94/4.17 f481_in(T32, T33) -> U16(f486_in(T32), T32, T33) 10.94/4.17 U16(f486_out1(T34), T32, T33) -> U17(f487_in(T34, T33), T32, T33, T34) 10.94/4.17 U17(f487_out1, T32, T33, T34) -> f481_out1(T34) 10.94/4.17 f541_in(T45, T46) -> U18(f486_in(T45), T45, T46) 10.94/4.17 U18(f486_out1(T47), T45, T46) -> U19(f567_in(T47, T46), T45, T46, T47) 10.94/4.17 U19(f567_out1, T45, T46, T47) -> f541_out1(T47) 10.94/4.17 f579_in(T52, T53) -> U20(f486_in(T52), T52, T53) 10.94/4.17 U20(f486_out1(T54), T52, T53) -> U21(f582_in(T54, T53), T52, T53, T54) 10.94/4.17 U21(f582_out1, T52, T53, T54) -> f579_out1(T54) 10.94/4.17 f594_in(T59, T60) -> U22(f486_in(T59), T59, T60) 10.94/4.17 U22(f486_out1(T61), T59, T60) -> U23(f597_in(T61, T60), T59, T60, T61) 10.94/4.17 U23(f597_out1, T59, T60, T61) -> f594_out1(T61) 10.94/4.17 f609_in(T66, T67) -> U24(f486_in(T66), T66, T67) 10.94/4.17 U24(f486_out1(T68), T66, T67) -> U25(f612_in(T68, T67), T66, T67, T68) 10.94/4.17 U25(f612_out1, T66, T67, T68) -> f609_out1(T68) 10.94/4.17 f657_in(T73, T74) -> U26(f486_in(T73), T73, T74) 10.94/4.17 U26(f486_out1(T75), T73, T74) -> U27(f674_in(T75, T74), T73, T74, T75) 10.94/4.17 U27(f674_out1, T73, T74, T75) -> f657_out1(T75) 10.94/4.17 f706_in(T80, T82, T81) -> U28(f486_in(T80), T80, T82, T81) 10.94/4.17 U28(f486_out1(T83), T80, T82, T81) -> U29(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.17 U29(f711_out1, T80, T82, T81, T83) -> f706_out1(T83) 10.94/4.17 10.94/4.17 Q is empty. 10.94/4.17 We have to consider all minimal (P,Q,R)-chains. 10.94/4.17 ---------------------------------------- 10.94/4.17 10.94/4.17 (100) 10.94/4.17 Obligation: 10.94/4.17 Q DP problem: 10.94/4.17 The TRS P consists of the following rules: 10.94/4.17 10.94/4.17 F294_IN -> F294_IN 10.94/4.17 10.94/4.17 The TRS R consists of the following rules: 10.94/4.17 10.94/4.17 f22_in(0) -> f22_out1(0) 10.94/4.17 f22_in(0) -> f22_out1(s(0)) 10.94/4.17 f22_in(T16) -> U1(f245_in(T16), T16) 10.94/4.17 U1(f245_out1(T17, X32), T16) -> f22_out1(s(s(T17))) 10.94/4.17 f294_in -> f294_out1(0, 0) 10.94/4.17 f294_in -> f294_out1(s(0), 0) 10.94/4.17 f294_in -> U2(f294_in) 10.94/4.17 U2(f294_out1(T27, X50)) -> f294_out1(s(s(T27)), s(X50)) 10.94/4.17 f501_in(0) -> f501_out1(0) 10.94/4.17 f501_in(s(0)) -> f501_out1(0) 10.94/4.17 f501_in(s(s(T40))) -> U3(f501_in(T40), s(s(T40))) 10.94/4.17 U3(f501_out1(X91), s(s(T40))) -> f501_out1(s(X91)) 10.94/4.17 f486_in(T37) -> U4(f501_in(T37), T37) 10.94/4.17 U4(f501_out1(X82), T37) -> f486_out1(s(X82)) 10.94/4.17 f247_in -> U5(f294_in) 10.94/4.17 U5(f294_out1(T23, X41)) -> f247_out1(T23, s(X41)) 10.94/4.17 f248_in(0, s(0)) -> f248_out1 10.94/4.17 f248_in(s(0), s(0)) -> f248_out1 10.94/4.17 f248_in(s(s(T32)), T33) -> U6(f481_in(T32, T33), s(s(T32)), T33) 10.94/4.17 U6(f481_out1(X73), s(s(T32)), T33) -> f248_out1 10.94/4.17 f487_in(0, s(s(0))) -> f487_out1 10.94/4.17 f487_in(s(0), s(s(0))) -> f487_out1 10.94/4.17 f487_in(s(s(T45)), T46) -> U7(f541_in(T45, T46), s(s(T45)), T46) 10.94/4.17 U7(f541_out1(X114), s(s(T45)), T46) -> f487_out1 10.94/4.17 f567_in(0, s(s(s(0)))) -> f567_out1 10.94/4.17 f567_in(s(0), s(s(s(0)))) -> f567_out1 10.94/4.17 f567_in(s(s(T52)), T53) -> U8(f579_in(T52, T53), s(s(T52)), T53) 10.94/4.17 U8(f579_out1(X137), s(s(T52)), T53) -> f567_out1 10.94/4.17 f582_in(0, s(s(s(s(0))))) -> f582_out1 10.94/4.17 f582_in(s(0), s(s(s(s(0))))) -> f582_out1 10.94/4.17 f582_in(s(s(T59)), T60) -> U9(f594_in(T59, T60), s(s(T59)), T60) 10.94/4.17 U9(f594_out1(X160), s(s(T59)), T60) -> f582_out1 10.94/4.17 f597_in(0, s(s(s(s(s(0)))))) -> f597_out1 10.94/4.17 f597_in(s(0), s(s(s(s(s(0)))))) -> f597_out1 10.94/4.17 f597_in(s(s(T66)), T67) -> U10(f609_in(T66, T67), s(s(T66)), T67) 10.94/4.17 U10(f609_out1(X183), s(s(T66)), T67) -> f597_out1 10.94/4.17 f612_in(0, s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.17 f612_in(s(0), s(s(s(s(s(s(0))))))) -> f612_out1 10.94/4.17 f612_in(s(s(T73)), T74) -> U11(f657_in(T73, T74), s(s(T73)), T74) 10.94/4.17 U11(f657_out1(X206), s(s(T73)), T74) -> f612_out1 10.94/4.17 f674_in(0, s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.17 f674_in(s(0), s(s(s(s(s(s(s(0)))))))) -> f674_out1 10.94/4.17 f674_in(s(s(T80)), T81) -> U12(f706_in(T80, s(s(s(s(s(s(s(0))))))), T81), s(s(T80)), T81) 10.94/4.17 U12(f706_out1(X229), s(s(T80)), T81) -> f674_out1 10.94/4.17 f711_in(0, T90, s(T90)) -> f711_out1 10.94/4.17 f711_in(s(0), T95, s(T95)) -> f711_out1 10.94/4.17 f711_in(s(s(T102)), T103, T104) -> U13(f706_in(T102, s(T103), T104), s(s(T102)), T103, T104) 10.94/4.17 U13(f706_out1(X252), s(s(T102)), T103, T104) -> f711_out1 10.94/4.17 f245_in(T16) -> U14(f247_in, T16) 10.94/4.17 U14(f247_out1(T17, T18), T16) -> U15(f248_in(T18, T16), T16, T17, T18) 10.94/4.17 U15(f248_out1, T16, T17, T18) -> f245_out1(T17, T18) 10.94/4.17 f481_in(T32, T33) -> U16(f486_in(T32), T32, T33) 10.94/4.17 U16(f486_out1(T34), T32, T33) -> U17(f487_in(T34, T33), T32, T33, T34) 10.94/4.17 U17(f487_out1, T32, T33, T34) -> f481_out1(T34) 10.94/4.17 f541_in(T45, T46) -> U18(f486_in(T45), T45, T46) 10.94/4.17 U18(f486_out1(T47), T45, T46) -> U19(f567_in(T47, T46), T45, T46, T47) 10.94/4.17 U19(f567_out1, T45, T46, T47) -> f541_out1(T47) 10.94/4.17 f579_in(T52, T53) -> U20(f486_in(T52), T52, T53) 10.94/4.17 U20(f486_out1(T54), T52, T53) -> U21(f582_in(T54, T53), T52, T53, T54) 10.94/4.17 U21(f582_out1, T52, T53, T54) -> f579_out1(T54) 10.94/4.17 f594_in(T59, T60) -> U22(f486_in(T59), T59, T60) 10.94/4.17 U22(f486_out1(T61), T59, T60) -> U23(f597_in(T61, T60), T59, T60, T61) 10.94/4.17 U23(f597_out1, T59, T60, T61) -> f594_out1(T61) 10.94/4.17 f609_in(T66, T67) -> U24(f486_in(T66), T66, T67) 10.94/4.17 U24(f486_out1(T68), T66, T67) -> U25(f612_in(T68, T67), T66, T67, T68) 10.94/4.17 U25(f612_out1, T66, T67, T68) -> f609_out1(T68) 10.94/4.17 f657_in(T73, T74) -> U26(f486_in(T73), T73, T74) 10.94/4.17 U26(f486_out1(T75), T73, T74) -> U27(f674_in(T75, T74), T73, T74, T75) 10.94/4.17 U27(f674_out1, T73, T74, T75) -> f657_out1(T75) 10.94/4.17 f706_in(T80, T82, T81) -> U28(f486_in(T80), T80, T82, T81) 10.94/4.17 U28(f486_out1(T83), T80, T82, T81) -> U29(f711_in(T83, T82, T81), T80, T82, T81, T83) 10.94/4.17 U29(f711_out1, T80, T82, T81, T83) -> f706_out1(T83) 10.94/4.17 10.94/4.17 Q is empty. 10.94/4.17 We have to consider all minimal (P,Q,R)-chains. 10.94/4.17 ---------------------------------------- 10.94/4.17 10.94/4.17 (101) UsableRulesProof (EQUIVALENT) 10.94/4.17 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. 10.94/4.17 ---------------------------------------- 10.94/4.17 10.94/4.17 (102) 10.94/4.17 Obligation: 10.94/4.17 Q DP problem: 10.94/4.17 The TRS P consists of the following rules: 10.94/4.17 10.94/4.17 F294_IN -> F294_IN 10.94/4.17 10.94/4.17 R is empty. 10.94/4.17 Q is empty. 10.94/4.17 We have to consider all minimal (P,Q,R)-chains. 10.94/4.17 ---------------------------------------- 10.94/4.17 10.94/4.17 (103) PrologToIRSwTTransformerProof (SOUND) 10.94/4.17 Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert 10.94/4.17 10.94/4.17 { 10.94/4.17 "root": 20, 10.94/4.17 "program": { 10.94/4.17 "directives": [], 10.94/4.17 "clauses": [ 10.94/4.17 [ 10.94/4.17 "(log2 X Y)", 10.94/4.17 "(log2 X (0) Y)" 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(log2 (0) I I)", 10.94/4.17 null 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(log2 (s (0)) I I)", 10.94/4.17 null 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(log2 (s (s X)) I Y)", 10.94/4.17 "(',' (half (s (s X)) X1) (log2 X1 (s I) Y))" 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(half (0) (0))", 10.94/4.17 null 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(half (s (0)) (0))", 10.94/4.17 null 10.94/4.17 ], 10.94/4.17 [ 10.94/4.17 "(half (s (s X)) (s Y))", 10.94/4.17 "(half X Y)" 10.94/4.17 ] 10.94/4.17 ] 10.94/4.17 }, 10.94/4.17 "graph": { 10.94/4.17 "nodes": { 10.94/4.17 "type": "Nodes", 10.94/4.17 "230": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "472": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T32"], 10.94/4.17 "free": ["X73"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "231": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "473": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T32"], 10.94/4.17 "free": ["X73"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "232": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "474": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 6, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T32"], 10.94/4.17 "free": ["X73"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "233": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 2, 10.94/4.17 "term": "(log2 T10 (0) T9)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T9"], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "750": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "234": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 2, 10.94/4.17 "term": "(log2 T10 (0) T9)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T9"], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "751": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "235": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "510": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "236": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "237": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "238": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T17)) X32) (log2 X32 (s (0)) T16))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T16"], 10.94/4.17 "free": ["X32"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "513": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "239": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "515": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "878": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T80)) X229) (log2 X229 (s (s (s (s (s (s (s (s (0))))))))) T81))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T80", 10.94/4.17 "T81" 10.94/4.17 ], 10.94/4.17 "free": ["X229"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "516": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "879": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "517": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "518": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "480": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "483": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "484": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "243": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X32"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "485": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "881": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T80)) X229) (log2 X229 (s T82) T81))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T80", 10.94/4.17 "T81", 10.94/4.17 "T82" 10.94/4.17 ], 10.94/4.17 "free": ["X229"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "244": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(log2 T18 (s (0)) T16)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T16", 10.94/4.17 "T18" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "882": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half (s (s T80)) X229)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T80"], 10.94/4.17 "free": ["X229"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "883": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "400": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "488": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "521": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "884": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "401": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "489": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "522": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 8, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "885": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "402": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "523": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "886": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "249": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X32"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "524": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "887": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "525": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "888": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "405": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T32)) X73) (log2 X73 (s (s (0))) T33))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T32", 10.94/4.17 "T33" 10.94/4.17 ], 10.94/4.17 "free": ["X73"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "889": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "408": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "529": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T45)) X114) (log2 X114 (s (s (s (0)))) T46))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T45", 10.94/4.17 "T46" 10.94/4.17 ], 10.94/4.17 "free": ["X114"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "409": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half (s (s T32)) X73)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T32"], 10.94/4.17 "free": ["X73"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "926": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "20": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(log2 T1 T2)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T2"], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "927": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 14, 10.94/4.17 "term": "(log2 T83 (s T82) T81)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T81", 10.94/4.17 "T82", 10.94/4.17 "T83" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "21": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 0, 10.94/4.17 "scope": 1, 10.94/4.17 "term": "(log2 T1 T2)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T2"], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "928": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "929": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "490": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "491": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "250": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X32"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "492": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 7, 10.94/4.17 "term": "(half T37 X82)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T37"], 10.94/4.17 "free": ["X82"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "251": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 3, 10.94/4.17 "term": "(half (s (s T17)) X32)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X32"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "494": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "496": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "530": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "410": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(log2 T34 (s (s (0))) T33)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T33", 10.94/4.17 "T34" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "498": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "499": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half T40 X91)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T40"], 10.94/4.17 "free": ["X91"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "930": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "931": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T102)) X252) (log2 X252 (s (s T103)) T104))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T102", 10.94/4.17 "T103", 10.94/4.17 "T104" 10.94/4.17 ], 10.94/4.17 "free": ["X252"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "536": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half (s (s T45)) X114)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": ["T45"], 10.94/4.17 "free": ["X114"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "932": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "537": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "266": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "267": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "542": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "268": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 4, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "269": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "544": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 1, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "545": { 10.94/4.17 "goal": [ 10.94/4.17 { 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }, 10.94/4.17 { 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 } 10.94/4.17 ], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "546": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "700": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 11, 10.94/4.17 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T60", 10.94/4.17 "T61" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "547": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "548": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "549": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 2, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "703": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "704": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "705": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "707": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(',' (half (s (s T66)) X183) (log2 X183 (s (s (s (s (s (s (0))))))) T67))" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T66", 10.94/4.17 "T67" 10.94/4.17 ], 10.94/4.17 "free": ["X183"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "708": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "270": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "271": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "392": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "272": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "393": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "273": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 5, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "394": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "274": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 6, 10.94/4.17 "scope": 4, 10.94/4.17 "term": "(half T23 X41)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": ["X41"], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "275": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": -1, 10.94/4.17 "scope": -1, 10.94/4.17 "term": "(true)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "550": { 10.94/4.17 "goal": [{ 10.94/4.17 "clause": 3, 10.94/4.17 "scope": 9, 10.94/4.17 "term": "(log2 T47 (s (s (s (0)))) T46)" 10.94/4.17 }], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.17 "ground": [ 10.94/4.17 "T46", 10.94/4.17 "T47" 10.94/4.17 ], 10.94/4.17 "free": [], 10.94/4.17 "exprvars": [] 10.94/4.17 } 10.94/4.17 }, 10.94/4.17 "276": { 10.94/4.17 "goal": [], 10.94/4.17 "kb": { 10.94/4.17 "nonunifying": [], 10.94/4.17 "intvars": {}, 10.94/4.17 "arithmetic": { 10.94/4.17 "type": "PlainIntegerRelationState", 10.94/4.17 "relations": [] 10.94/4.17 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "551": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "277": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "398": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T16", 10.94/4.18 "T18" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "552": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "278": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(half T27 X50)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": ["X50"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "399": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T16", 10.94/4.18 "T18" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "553": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "279": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "554": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(',' (half (s (s T52)) X137) (log2 X137 (s (s (s (s (0))))) T53))" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T52", 10.94/4.18 "T53" 10.94/4.18 ], 10.94/4.18 "free": ["X137"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "675": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "555": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "676": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "556": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(half (s (s T52)) X137)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T52"], 10.94/4.18 "free": ["X137"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "677": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "710": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(half (s (s T66)) X183)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T66"], 10.94/4.18 "free": ["X183"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "557": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "558": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "679": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(',' (half (s (s T59)) X160) (log2 X160 (s (s (s (s (s (0)))))) T60))" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T59", 10.94/4.18 "T60" 10.94/4.18 ], 10.94/4.18 "free": ["X160"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "712": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "559": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "716": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "717": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "718": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "280": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T16", 10.94/4.18 "T18" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "281": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T16", 10.94/4.18 "T18" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "282": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 5, 10.94/4.18 "term": "(log2 T18 (s (0)) T16)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T16", 10.94/4.18 "T18" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "680": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "560": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "561": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "562": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "563": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "564": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "565": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 10, 10.94/4.18 "term": "(log2 T54 (s (s (s (s (0))))) T53)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T53", 10.94/4.18 "T54" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "686": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(half (s (s T59)) X160)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T59"], 10.94/4.18 "free": ["X160"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "687": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T60", 10.94/4.18 "T61" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "722": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "723": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "724": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "727": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "728": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 12, 10.94/4.18 "term": "(log2 T68 (s (s (s (s (s (s (0))))))) T67)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T67", 10.94/4.18 "T68" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "172": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T9"], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "690": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T60", 10.94/4.18 "T61" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "691": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T60", 10.94/4.18 "T61" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "176": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T9"], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "693": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T60", 10.94/4.18 "T61" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "696": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "697": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "698": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "699": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 11, 10.94/4.18 "term": "(log2 T61 (s (s (s (s (s (0)))))) T60)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T60", 10.94/4.18 "T61" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "732": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "733": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "734": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "736": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(',' (half (s (s T73)) X206) (log2 X206 (s (s (s (s (s (s (s (0)))))))) T74))" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T73", 10.94/4.18 "T74" 10.94/4.18 ], 10.94/4.18 "free": ["X206"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "738": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "739": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(half (s (s T73)) X206)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T73"], 10.94/4.18 "free": ["X206"], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "180": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T9"], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "182": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 2, 10.94/4.18 "term": "(log2 T10 (0) T9)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": ["T9"], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "740": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "741": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "500": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "742": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 1, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "743": { 10.94/4.18 "goal": [ 10.94/4.18 { 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 } 10.94/4.18 ], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "744": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "745": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "746": { 10.94/4.18 "goal": [], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "747": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 2, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "748": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": 3, 10.94/4.18 "scope": 13, 10.94/4.18 "term": "(log2 T75 (s (s (s (s (s (s (s (0)))))))) T74)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [ 10.94/4.18 "T74", 10.94/4.18 "T75" 10.94/4.18 ], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "749": { 10.94/4.18 "goal": [{ 10.94/4.18 "clause": -1, 10.94/4.18 "scope": -1, 10.94/4.18 "term": "(true)" 10.94/4.18 }], 10.94/4.18 "kb": { 10.94/4.18 "nonunifying": [], 10.94/4.18 "intvars": {}, 10.94/4.18 "arithmetic": { 10.94/4.18 "type": "PlainIntegerRelationState", 10.94/4.18 "relations": [] 10.94/4.18 }, 10.94/4.18 "ground": [], 10.94/4.18 "free": [], 10.94/4.18 "exprvars": [] 10.94/4.18 } 10.94/4.18 } 10.94/4.18 }, 10.94/4.18 "edges": [ 10.94/4.18 { 10.94/4.18 "from": 20, 10.94/4.18 "to": 21, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 21, 10.94/4.18 "to": 172, 10.94/4.18 "label": "ONLY EVAL with clause\nlog2(X8, X9) :- log2(X8, 0, X9).\nand substitutionT1 -> T10,\nX8 -> T10,\nT2 -> T9,\nX9 -> T9,\nT8 -> T10" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 172, 10.94/4.18 "to": 176, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 176, 10.94/4.18 "to": 180, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 176, 10.94/4.18 "to": 182, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 180, 10.94/4.18 "to": 230, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X16, X16).\nand substitutionT10 -> 0,\nX16 -> 0,\nT9 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 180, 10.94/4.18 "to": 231, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 182, 10.94/4.18 "to": 233, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 182, 10.94/4.18 "to": 234, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 230, 10.94/4.18 "to": 232, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 233, 10.94/4.18 "to": 235, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X21, X21).\nand substitutionT10 -> s(0),\nX21 -> 0,\nT9 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 233, 10.94/4.18 "to": 236, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 234, 10.94/4.18 "to": 238, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X29)), X30, X31) :- ','(half(s(s(X29)), X32), log2(X32, s(X30), X31)).\nand substitutionX29 -> T17,\nT10 -> s(s(T17)),\nX30 -> 0,\nT9 -> T16,\nX31 -> T16,\nT15 -> T17" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 234, 10.94/4.18 "to": 239, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 235, 10.94/4.18 "to": 237, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 238, 10.94/4.18 "to": 243, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 238, 10.94/4.18 "to": 244, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT17 is ground\nT18 is ground\nreplacements:X32 -> T18" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 243, 10.94/4.18 "to": 249, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 244, 10.94/4.18 "to": 280, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 249, 10.94/4.18 "to": 250, 10.94/4.18 "label": "BACKTRACK\nfor clause: half(0, 0)because of non-unification" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 250, 10.94/4.18 "to": 251, 10.94/4.18 "label": "BACKTRACK\nfor clause: half(s(0), 0)because of non-unification" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 251, 10.94/4.18 "to": 266, 10.94/4.18 "label": "ONLY EVAL with clause\nhalf(s(s(X39)), s(X40)) :- half(X39, X40).\nand substitutionT17 -> T23,\nX39 -> T23,\nX40 -> X41,\nX32 -> s(X41),\nT22 -> T23" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 266, 10.94/4.18 "to": 267, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 267, 10.94/4.18 "to": 268, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 267, 10.94/4.18 "to": 269, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 268, 10.94/4.18 "to": 270, 10.94/4.18 "label": "EVAL with clause\nhalf(0, 0).\nand substitutionT23 -> 0,\nX41 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 268, 10.94/4.18 "to": 271, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 269, 10.94/4.18 "to": 273, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 269, 10.94/4.18 "to": 274, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 270, 10.94/4.18 "to": 272, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 273, 10.94/4.18 "to": 275, 10.94/4.18 "label": "EVAL with clause\nhalf(s(0), 0).\nand substitutionT23 -> s(0),\nX41 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 273, 10.94/4.18 "to": 276, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 274, 10.94/4.18 "to": 278, 10.94/4.18 "label": "EVAL with clause\nhalf(s(s(X48)), s(X49)) :- half(X48, X49).\nand substitutionX48 -> T27,\nT23 -> s(s(T27)),\nX49 -> X50,\nX41 -> s(X50),\nT26 -> T27" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 274, 10.94/4.18 "to": 279, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 275, 10.94/4.18 "to": 277, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 278, 10.94/4.18 "to": 266, 10.94/4.18 "label": "INSTANCE with matching:\nT23 -> T27\nX41 -> X50" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 280, 10.94/4.18 "to": 281, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 280, 10.94/4.18 "to": 282, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 281, 10.94/4.18 "to": 392, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X57, X57).\nand substitutionT18 -> 0,\nX57 -> s(0),\nT16 -> s(0)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 281, 10.94/4.18 "to": 393, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 282, 10.94/4.18 "to": 398, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 282, 10.94/4.18 "to": 399, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 392, 10.94/4.18 "to": 394, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 398, 10.94/4.18 "to": 400, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X62, X62).\nand substitutionT18 -> s(0),\nX62 -> s(0),\nT16 -> s(0)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 398, 10.94/4.18 "to": 401, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 399, 10.94/4.18 "to": 405, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X70)), X71, X72) :- ','(half(s(s(X70)), X73), log2(X73, s(X71), X72)).\nand substitutionX70 -> T32,\nT18 -> s(s(T32)),\nX71 -> s(0),\nT16 -> T33,\nX72 -> T33" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 399, 10.94/4.18 "to": 408, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 400, 10.94/4.18 "to": 402, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 405, 10.94/4.18 "to": 409, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 405, 10.94/4.18 "to": 410, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT32 is ground\nT34 is ground\nreplacements:X73 -> T34" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 409, 10.94/4.18 "to": 472, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 410, 10.94/4.18 "to": 510, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 472, 10.94/4.18 "to": 473, 10.94/4.18 "label": "BACKTRACK\nfor clause: half(0, 0)because of non-unification" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 473, 10.94/4.18 "to": 474, 10.94/4.18 "label": "BACKTRACK\nfor clause: half(s(0), 0)because of non-unification" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 474, 10.94/4.18 "to": 480, 10.94/4.18 "label": "ONLY EVAL with clause\nhalf(s(s(X80)), s(X81)) :- half(X80, X81).\nand substitutionT32 -> T37,\nX80 -> T37,\nX81 -> X82,\nX73 -> s(X82)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 480, 10.94/4.18 "to": 483, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 483, 10.94/4.18 "to": 484, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 483, 10.94/4.18 "to": 485, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 484, 10.94/4.18 "to": 488, 10.94/4.18 "label": "EVAL with clause\nhalf(0, 0).\nand substitutionT37 -> 0,\nX82 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 484, 10.94/4.18 "to": 489, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 485, 10.94/4.18 "to": 491, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 485, 10.94/4.18 "to": 492, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 488, 10.94/4.18 "to": 490, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 491, 10.94/4.18 "to": 494, 10.94/4.18 "label": "EVAL with clause\nhalf(s(0), 0).\nand substitutionT37 -> s(0),\nX82 -> 0" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 491, 10.94/4.18 "to": 496, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 492, 10.94/4.18 "to": 499, 10.94/4.18 "label": "EVAL with clause\nhalf(s(s(X89)), s(X90)) :- half(X89, X90).\nand substitutionX89 -> T40,\nT37 -> s(s(T40)),\nX90 -> X91,\nX82 -> s(X91)" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 492, 10.94/4.18 "to": 500, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 494, 10.94/4.18 "to": 498, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 499, 10.94/4.18 "to": 480, 10.94/4.18 "label": "INSTANCE with matching:\nT37 -> T40\nX82 -> X91" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 510, 10.94/4.18 "to": 513, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 510, 10.94/4.18 "to": 515, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 513, 10.94/4.18 "to": 516, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X98, X98).\nand substitutionT34 -> 0,\nX98 -> s(s(0)),\nT33 -> s(s(0))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 513, 10.94/4.18 "to": 517, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 515, 10.94/4.18 "to": 521, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 515, 10.94/4.18 "to": 522, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 516, 10.94/4.18 "to": 518, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 521, 10.94/4.18 "to": 523, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X103, X103).\nand substitutionT34 -> s(0),\nX103 -> s(s(0)),\nT33 -> s(s(0))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 521, 10.94/4.18 "to": 524, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 522, 10.94/4.18 "to": 529, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X111)), X112, X113) :- ','(half(s(s(X111)), X114), log2(X114, s(X112), X113)).\nand substitutionX111 -> T45,\nT34 -> s(s(T45)),\nX112 -> s(s(0)),\nT33 -> T46,\nX113 -> T46" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 522, 10.94/4.18 "to": 530, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 523, 10.94/4.18 "to": 525, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 529, 10.94/4.18 "to": 536, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 529, 10.94/4.18 "to": 537, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT45 is ground\nT47 is ground\nreplacements:X114 -> T47" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 536, 10.94/4.18 "to": 409, 10.94/4.18 "label": "INSTANCE with matching:\nT32 -> T45\nX73 -> X114" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 537, 10.94/4.18 "to": 542, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 542, 10.94/4.18 "to": 544, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 542, 10.94/4.18 "to": 545, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 544, 10.94/4.18 "to": 546, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X121, X121).\nand substitutionT47 -> 0,\nX121 -> s(s(s(0))),\nT46 -> s(s(s(0)))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 544, 10.94/4.18 "to": 547, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 545, 10.94/4.18 "to": 549, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 545, 10.94/4.18 "to": 550, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 546, 10.94/4.18 "to": 548, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 549, 10.94/4.18 "to": 551, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X126, X126).\nand substitutionT47 -> s(0),\nX126 -> s(s(s(0))),\nT46 -> s(s(s(0)))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 549, 10.94/4.18 "to": 552, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 550, 10.94/4.18 "to": 554, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X134)), X135, X136) :- ','(half(s(s(X134)), X137), log2(X137, s(X135), X136)).\nand substitutionX134 -> T52,\nT47 -> s(s(T52)),\nX135 -> s(s(s(0))),\nT46 -> T53,\nX136 -> T53" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 550, 10.94/4.18 "to": 555, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 551, 10.94/4.18 "to": 553, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 554, 10.94/4.18 "to": 556, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 554, 10.94/4.18 "to": 557, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT52 is ground\nT54 is ground\nreplacements:X137 -> T54" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 556, 10.94/4.18 "to": 409, 10.94/4.18 "label": "INSTANCE with matching:\nT32 -> T52\nX73 -> X137" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 557, 10.94/4.18 "to": 558, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 558, 10.94/4.18 "to": 559, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 558, 10.94/4.18 "to": 560, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 559, 10.94/4.18 "to": 561, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X144, X144).\nand substitutionT54 -> 0,\nX144 -> s(s(s(s(0)))),\nT53 -> s(s(s(s(0))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 559, 10.94/4.18 "to": 562, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 560, 10.94/4.18 "to": 564, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 560, 10.94/4.18 "to": 565, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 561, 10.94/4.18 "to": 563, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 564, 10.94/4.18 "to": 675, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X149, X149).\nand substitutionT54 -> s(0),\nX149 -> s(s(s(s(0)))),\nT53 -> s(s(s(s(0))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 564, 10.94/4.18 "to": 676, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 565, 10.94/4.18 "to": 679, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X157)), X158, X159) :- ','(half(s(s(X157)), X160), log2(X160, s(X158), X159)).\nand substitutionX157 -> T59,\nT54 -> s(s(T59)),\nX158 -> s(s(s(s(0)))),\nT53 -> T60,\nX159 -> T60" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 565, 10.94/4.18 "to": 680, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 675, 10.94/4.18 "to": 677, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 679, 10.94/4.18 "to": 686, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 679, 10.94/4.18 "to": 687, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT59 is ground\nT61 is ground\nreplacements:X160 -> T61" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 686, 10.94/4.18 "to": 409, 10.94/4.18 "label": "INSTANCE with matching:\nT32 -> T59\nX73 -> X160" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 687, 10.94/4.18 "to": 690, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 690, 10.94/4.18 "to": 691, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 690, 10.94/4.18 "to": 693, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 691, 10.94/4.18 "to": 696, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X167, X167).\nand substitutionT61 -> 0,\nX167 -> s(s(s(s(s(0))))),\nT60 -> s(s(s(s(s(0)))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 691, 10.94/4.18 "to": 697, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 693, 10.94/4.18 "to": 699, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 693, 10.94/4.18 "to": 700, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 696, 10.94/4.18 "to": 698, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 699, 10.94/4.18 "to": 703, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X172, X172).\nand substitutionT61 -> s(0),\nX172 -> s(s(s(s(s(0))))),\nT60 -> s(s(s(s(s(0)))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 699, 10.94/4.18 "to": 704, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 700, 10.94/4.18 "to": 707, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X180)), X181, X182) :- ','(half(s(s(X180)), X183), log2(X183, s(X181), X182)).\nand substitutionX180 -> T66,\nT61 -> s(s(T66)),\nX181 -> s(s(s(s(s(0))))),\nT60 -> T67,\nX182 -> T67" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 700, 10.94/4.18 "to": 708, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 703, 10.94/4.18 "to": 705, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 707, 10.94/4.18 "to": 710, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 707, 10.94/4.18 "to": 712, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT66 is ground\nT68 is ground\nreplacements:X183 -> T68" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 710, 10.94/4.18 "to": 409, 10.94/4.18 "label": "INSTANCE with matching:\nT32 -> T66\nX73 -> X183" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 712, 10.94/4.18 "to": 716, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 716, 10.94/4.18 "to": 717, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 716, 10.94/4.18 "to": 718, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 717, 10.94/4.18 "to": 722, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X190, X190).\nand substitutionT68 -> 0,\nX190 -> s(s(s(s(s(s(0)))))),\nT67 -> s(s(s(s(s(s(0))))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 717, 10.94/4.18 "to": 723, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 718, 10.94/4.18 "to": 727, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 718, 10.94/4.18 "to": 728, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 722, 10.94/4.18 "to": 724, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 727, 10.94/4.18 "to": 732, 10.94/4.18 "label": "EVAL with clause\nlog2(s(0), X195, X195).\nand substitutionT68 -> s(0),\nX195 -> s(s(s(s(s(s(0)))))),\nT67 -> s(s(s(s(s(s(0))))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 727, 10.94/4.18 "to": 733, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 728, 10.94/4.18 "to": 736, 10.94/4.18 "label": "EVAL with clause\nlog2(s(s(X203)), X204, X205) :- ','(half(s(s(X203)), X206), log2(X206, s(X204), X205)).\nand substitutionX203 -> T73,\nT68 -> s(s(T73)),\nX204 -> s(s(s(s(s(s(0)))))),\nT67 -> T74,\nX205 -> T74" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 728, 10.94/4.18 "to": 738, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 732, 10.94/4.18 "to": 734, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 736, 10.94/4.18 "to": 739, 10.94/4.18 "label": "SPLIT 1" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 736, 10.94/4.18 "to": 740, 10.94/4.18 "label": "SPLIT 2\nnew knowledge:\nT73 is ground\nT75 is ground\nreplacements:X206 -> T75" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 739, 10.94/4.18 "to": 409, 10.94/4.18 "label": "INSTANCE with matching:\nT32 -> T73\nX73 -> X206" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 740, 10.94/4.18 "to": 741, 10.94/4.18 "label": "CASE" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 741, 10.94/4.18 "to": 742, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 741, 10.94/4.18 "to": 743, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 742, 10.94/4.18 "to": 744, 10.94/4.18 "label": "EVAL with clause\nlog2(0, X213, X213).\nand substitutionT75 -> 0,\nX213 -> s(s(s(s(s(s(s(0))))))),\nT74 -> s(s(s(s(s(s(s(0)))))))" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 742, 10.94/4.18 "to": 745, 10.94/4.18 "label": "EVAL-BACKTRACK" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 743, 10.94/4.18 "to": 747, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 743, 10.94/4.18 "to": 748, 10.94/4.18 "label": "PARALLEL" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 744, 10.94/4.18 "to": 746, 10.94/4.18 "label": "SUCCESS" 10.94/4.18 }, 10.94/4.18 { 10.94/4.18 "from": 747, 10.94/4.18 "to": 749, 10.94/4.19 "label": "EVAL with clause\nlog2(s(0), X218, X218).\nand substitutionT75 -> s(0),\nX218 -> s(s(s(s(s(s(s(0))))))),\nT74 -> s(s(s(s(s(s(s(0)))))))" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 747, 10.94/4.19 "to": 750, 10.94/4.19 "label": "EVAL-BACKTRACK" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 748, 10.94/4.19 "to": 878, 10.94/4.19 "label": "EVAL with clause\nlog2(s(s(X226)), X227, X228) :- ','(half(s(s(X226)), X229), log2(X229, s(X227), X228)).\nand substitutionX226 -> T80,\nT75 -> s(s(T80)),\nX227 -> s(s(s(s(s(s(s(0))))))),\nT74 -> T81,\nX228 -> T81" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 748, 10.94/4.19 "to": 879, 10.94/4.19 "label": "EVAL-BACKTRACK" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 749, 10.94/4.19 "to": 751, 10.94/4.19 "label": "SUCCESS" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 878, 10.94/4.19 "to": 881, 10.94/4.19 "label": "GENERALIZATION\nT82 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT82 is ground" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 881, 10.94/4.19 "to": 882, 10.94/4.19 "label": "SPLIT 1" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 881, 10.94/4.19 "to": 883, 10.94/4.19 "label": "SPLIT 2\nnew knowledge:\nT80 is ground\nT83 is ground\nreplacements:X229 -> T83" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 882, 10.94/4.19 "to": 409, 10.94/4.19 "label": "INSTANCE with matching:\nT32 -> T80\nX73 -> X229" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 883, 10.94/4.19 "to": 884, 10.94/4.19 "label": "CASE" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 884, 10.94/4.19 "to": 885, 10.94/4.19 "label": "PARALLEL" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 884, 10.94/4.19 "to": 886, 10.94/4.19 "label": "PARALLEL" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 885, 10.94/4.19 "to": 887, 10.94/4.19 "label": "EVAL with clause\nlog2(0, X236, X236).\nand substitutionT83 -> 0,\nT82 -> T90,\nX236 -> s(T90),\nT81 -> s(T90)" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 885, 10.94/4.19 "to": 888, 10.94/4.19 "label": "EVAL-BACKTRACK" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 886, 10.94/4.19 "to": 926, 10.94/4.19 "label": "PARALLEL" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 886, 10.94/4.19 "to": 927, 10.94/4.19 "label": "PARALLEL" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 887, 10.94/4.19 "to": 889, 10.94/4.19 "label": "SUCCESS" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 926, 10.94/4.19 "to": 928, 10.94/4.19 "label": "EVAL with clause\nlog2(s(0), X241, X241).\nand substitutionT83 -> s(0),\nT82 -> T95,\nX241 -> s(T95),\nT81 -> s(T95)" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 926, 10.94/4.19 "to": 929, 10.94/4.19 "label": "EVAL-BACKTRACK" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 927, 10.94/4.19 "to": 931, 10.94/4.19 "label": "EVAL with clause\nlog2(s(s(X249)), X250, X251) :- ','(half(s(s(X249)), X252), log2(X252, s(X250), X251)).\nand substitutionX249 -> T102,\nT83 -> s(s(T102)),\nT82 -> T103,\nX250 -> s(T103),\nT81 -> T104,\nX251 -> T104" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 927, 10.94/4.19 "to": 932, 10.94/4.19 "label": "EVAL-BACKTRACK" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 928, 10.94/4.19 "to": 930, 10.94/4.19 "label": "SUCCESS" 10.94/4.19 }, 10.94/4.19 { 10.94/4.19 "from": 931, 10.94/4.19 "to": 881, 10.94/4.19 "label": "INSTANCE with matching:\nT80 -> T102\nX229 -> X252\nT82 -> s(T103)\nT81 -> T104" 10.94/4.19 } 10.94/4.19 ], 10.94/4.19 "type": "Graph" 10.94/4.19 } 10.94/4.19 } 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (104) 10.94/4.19 Complex Obligation (AND) 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (105) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f485_in(T37) -> f492_in(T37) :|: TRUE 10.94/4.19 f492_out(x) -> f485_out(x) :|: TRUE 10.94/4.19 f491_out(x1) -> f485_out(x1) :|: TRUE 10.94/4.19 f485_in(x2) -> f491_in(x2) :|: TRUE 10.94/4.19 f483_in(x3) -> f484_in(x3) :|: TRUE 10.94/4.19 f484_out(x4) -> f483_out(x4) :|: TRUE 10.94/4.19 f483_in(x5) -> f485_in(x5) :|: TRUE 10.94/4.19 f485_out(x6) -> f483_out(x6) :|: TRUE 10.94/4.19 f480_in(x7) -> f483_in(x7) :|: TRUE 10.94/4.19 f483_out(x8) -> f480_out(x8) :|: TRUE 10.94/4.19 f480_out(T40) -> f499_out(T40) :|: TRUE 10.94/4.19 f499_in(x9) -> f480_in(x9) :|: TRUE 10.94/4.19 f492_in(x10) -> f500_in :|: TRUE 10.94/4.19 f492_in(s(s(x11))) -> f499_in(x11) :|: TRUE 10.94/4.19 f500_out -> f492_out(x12) :|: TRUE 10.94/4.19 f499_out(x13) -> f492_out(s(s(x13))) :|: TRUE 10.94/4.19 f20_in(T2) -> f21_in(T2) :|: TRUE 10.94/4.19 f21_out(x14) -> f20_out(x14) :|: TRUE 10.94/4.19 f172_out(T9) -> f21_out(T9) :|: TRUE 10.94/4.19 f21_in(x15) -> f172_in(x15) :|: TRUE 10.94/4.19 f172_in(x16) -> f176_in(x16) :|: TRUE 10.94/4.19 f176_out(x17) -> f172_out(x17) :|: TRUE 10.94/4.19 f182_out(x18) -> f176_out(x18) :|: TRUE 10.94/4.19 f180_out(x19) -> f176_out(x19) :|: TRUE 10.94/4.19 f176_in(x20) -> f182_in(x20) :|: TRUE 10.94/4.19 f176_in(x21) -> f180_in(x21) :|: TRUE 10.94/4.19 f182_in(x22) -> f233_in(x22) :|: TRUE 10.94/4.19 f234_out(x23) -> f182_out(x23) :|: TRUE 10.94/4.19 f233_out(x24) -> f182_out(x24) :|: TRUE 10.94/4.19 f182_in(x25) -> f234_in(x25) :|: TRUE 10.94/4.19 f239_out -> f234_out(x26) :|: TRUE 10.94/4.19 f238_out(T16) -> f234_out(T16) :|: TRUE 10.94/4.19 f234_in(x27) -> f239_in :|: TRUE 10.94/4.19 f234_in(x28) -> f238_in(x28) :|: TRUE 10.94/4.19 f238_in(x29) -> f243_in :|: TRUE 10.94/4.19 f243_out -> f244_in(x30, x31) :|: TRUE 10.94/4.19 f244_out(x32, x33) -> f238_out(x33) :|: TRUE 10.94/4.19 f280_out(x34, x35) -> f244_out(x34, x35) :|: TRUE 10.94/4.19 f244_in(x36, x37) -> f280_in(x36, x37) :|: TRUE 10.94/4.19 f280_in(x38, x39) -> f281_in(x38, x39) :|: TRUE 10.94/4.19 f281_out(x40, x41) -> f280_out(x40, x41) :|: TRUE 10.94/4.19 f282_out(x42, x43) -> f280_out(x42, x43) :|: TRUE 10.94/4.19 f280_in(x44, x45) -> f282_in(x44, x45) :|: TRUE 10.94/4.19 f398_out(x46, x47) -> f282_out(x46, x47) :|: TRUE 10.94/4.19 f282_in(x48, x49) -> f398_in(x48, x49) :|: TRUE 10.94/4.19 f399_out(x50, x51) -> f282_out(x50, x51) :|: TRUE 10.94/4.19 f282_in(x52, x53) -> f399_in(x52, x53) :|: TRUE 10.94/4.19 f399_in(x54, x55) -> f408_in :|: TRUE 10.94/4.19 f408_out -> f399_out(x56, x57) :|: TRUE 10.94/4.19 f399_in(s(s(T32)), T33) -> f405_in(T32, T33) :|: TRUE 10.94/4.19 f405_out(x58, x59) -> f399_out(s(s(x58)), x59) :|: TRUE 10.94/4.19 f405_in(x60, x61) -> f409_in(x60) :|: TRUE 10.94/4.19 f410_out(x62, x63) -> f405_out(x64, x63) :|: TRUE 10.94/4.19 f409_out(x65) -> f410_in(x66, x67) :|: TRUE 10.94/4.19 f510_out(x68, x69) -> f410_out(x68, x69) :|: TRUE 10.94/4.19 f410_in(x70, x71) -> f510_in(x70, x71) :|: TRUE 10.94/4.19 f515_out(x72, x73) -> f510_out(x72, x73) :|: TRUE 10.94/4.19 f510_in(x74, x75) -> f515_in(x74, x75) :|: TRUE 10.94/4.19 f510_in(x76, x77) -> f513_in(x76, x77) :|: TRUE 10.94/4.19 f513_out(x78, x79) -> f510_out(x78, x79) :|: TRUE 10.94/4.19 f515_in(x80, x81) -> f522_in(x80, x81) :|: TRUE 10.94/4.19 f522_out(x82, x83) -> f515_out(x82, x83) :|: TRUE 10.94/4.19 f515_in(x84, x85) -> f521_in(x84, x85) :|: TRUE 10.94/4.19 f521_out(x86, x87) -> f515_out(x86, x87) :|: TRUE 10.94/4.19 f530_out -> f522_out(x88, x89) :|: TRUE 10.94/4.19 f529_out(T45, T46) -> f522_out(s(s(T45)), T46) :|: TRUE 10.94/4.19 f522_in(x90, x91) -> f530_in :|: TRUE 10.94/4.19 f522_in(s(s(x92)), x93) -> f529_in(x92, x93) :|: TRUE 10.94/4.19 f537_out(x94, x95) -> f529_out(x96, x95) :|: TRUE 10.94/4.19 f536_out(x97) -> f537_in(x98, x99) :|: TRUE 10.94/4.19 f529_in(x100, x101) -> f536_in(x100) :|: TRUE 10.94/4.19 f542_out(x102, x103) -> f537_out(x102, x103) :|: TRUE 10.94/4.19 f537_in(x104, x105) -> f542_in(x104, x105) :|: TRUE 10.94/4.19 f542_in(x106, x107) -> f544_in(x106, x107) :|: TRUE 10.94/4.19 f542_in(x108, x109) -> f545_in(x108, x109) :|: TRUE 10.94/4.19 f544_out(x110, x111) -> f542_out(x110, x111) :|: TRUE 10.94/4.19 f545_out(x112, x113) -> f542_out(x112, x113) :|: TRUE 10.94/4.19 f545_in(x114, x115) -> f550_in(x114, x115) :|: TRUE 10.94/4.19 f550_out(x116, x117) -> f545_out(x116, x117) :|: TRUE 10.94/4.19 f549_out(x118, x119) -> f545_out(x118, x119) :|: TRUE 10.94/4.19 f545_in(x120, x121) -> f549_in(x120, x121) :|: TRUE 10.94/4.19 f555_out -> f550_out(x122, x123) :|: TRUE 10.94/4.19 f550_in(s(s(T52)), T53) -> f554_in(T52, T53) :|: TRUE 10.94/4.19 f554_out(x124, x125) -> f550_out(s(s(x124)), x125) :|: TRUE 10.94/4.19 f550_in(x126, x127) -> f555_in :|: TRUE 10.94/4.19 f556_out(x128) -> f557_in(x129, x130) :|: TRUE 10.94/4.19 f557_out(x131, x132) -> f554_out(x133, x132) :|: TRUE 10.94/4.19 f554_in(x134, x135) -> f556_in(x134) :|: TRUE 10.94/4.19 f557_in(x136, x137) -> f558_in(x136, x137) :|: TRUE 10.94/4.19 f558_out(x138, x139) -> f557_out(x138, x139) :|: TRUE 10.94/4.19 f558_in(x140, x141) -> f559_in(x140, x141) :|: TRUE 10.94/4.19 f559_out(x142, x143) -> f558_out(x142, x143) :|: TRUE 10.94/4.19 f560_out(x144, x145) -> f558_out(x144, x145) :|: TRUE 10.94/4.19 f558_in(x146, x147) -> f560_in(x146, x147) :|: TRUE 10.94/4.19 f560_in(x148, x149) -> f565_in(x148, x149) :|: TRUE 10.94/4.19 f564_out(x150, x151) -> f560_out(x150, x151) :|: TRUE 10.94/4.19 f560_in(x152, x153) -> f564_in(x152, x153) :|: TRUE 10.94/4.19 f565_out(x154, x155) -> f560_out(x154, x155) :|: TRUE 10.94/4.19 f679_out(T59, T60) -> f565_out(s(s(T59)), T60) :|: TRUE 10.94/4.19 f680_out -> f565_out(x156, x157) :|: TRUE 10.94/4.19 f565_in(x158, x159) -> f680_in :|: TRUE 10.94/4.19 f565_in(s(s(x160)), x161) -> f679_in(x160, x161) :|: TRUE 10.94/4.19 f679_in(x162, x163) -> f686_in(x162) :|: TRUE 10.94/4.19 f687_out(x164, x165) -> f679_out(x166, x165) :|: TRUE 10.94/4.19 f686_out(x167) -> f687_in(x168, x169) :|: TRUE 10.94/4.19 f409_out(x170) -> f686_out(x170) :|: TRUE 10.94/4.19 f686_in(x171) -> f409_in(x171) :|: TRUE 10.94/4.19 f409_in(x172) -> f472_in(x172) :|: TRUE 10.94/4.19 f472_out(x173) -> f409_out(x173) :|: TRUE 10.94/4.19 f473_out(x174) -> f472_out(x174) :|: TRUE 10.94/4.19 f472_in(x175) -> f473_in(x175) :|: TRUE 10.94/4.19 f474_out(x176) -> f473_out(x176) :|: TRUE 10.94/4.19 f473_in(x177) -> f474_in(x177) :|: TRUE 10.94/4.19 f480_out(x178) -> f474_out(x178) :|: TRUE 10.94/4.19 f474_in(x179) -> f480_in(x179) :|: TRUE 10.94/4.19 f687_in(x180, x181) -> f690_in(x180, x181) :|: TRUE 10.94/4.19 f690_out(x182, x183) -> f687_out(x182, x183) :|: TRUE 10.94/4.19 f690_in(x184, x185) -> f693_in(x184, x185) :|: TRUE 10.94/4.19 f691_out(x186, x187) -> f690_out(x186, x187) :|: TRUE 10.94/4.19 f693_out(x188, x189) -> f690_out(x188, x189) :|: TRUE 10.94/4.19 f690_in(x190, x191) -> f691_in(x190, x191) :|: TRUE 10.94/4.19 f693_in(x192, x193) -> f699_in(x192, x193) :|: TRUE 10.94/4.19 f699_out(x194, x195) -> f693_out(x194, x195) :|: TRUE 10.94/4.19 f700_out(x196, x197) -> f693_out(x196, x197) :|: TRUE 10.94/4.19 f693_in(x198, x199) -> f700_in(x198, x199) :|: TRUE 10.94/4.19 f700_in(s(s(T66)), T67) -> f707_in(T66, T67) :|: TRUE 10.94/4.19 f707_out(x200, x201) -> f700_out(s(s(x200)), x201) :|: TRUE 10.94/4.19 f700_in(x202, x203) -> f708_in :|: TRUE 10.94/4.19 f708_out -> f700_out(x204, x205) :|: TRUE 10.94/4.19 f712_out(x206, x207) -> f707_out(x208, x207) :|: TRUE 10.94/4.19 f710_out(x209) -> f712_in(x210, x211) :|: TRUE 10.94/4.19 f707_in(x212, x213) -> f710_in(x212) :|: TRUE 10.94/4.19 f712_in(x214, x215) -> f716_in(x214, x215) :|: TRUE 10.94/4.19 f716_out(x216, x217) -> f712_out(x216, x217) :|: TRUE 10.94/4.19 f716_in(x218, x219) -> f717_in(x218, x219) :|: TRUE 10.94/4.19 f717_out(x220, x221) -> f716_out(x220, x221) :|: TRUE 10.94/4.19 f716_in(x222, x223) -> f718_in(x222, x223) :|: TRUE 10.94/4.19 f718_out(x224, x225) -> f716_out(x224, x225) :|: TRUE 10.94/4.19 f718_in(x226, x227) -> f728_in(x226, x227) :|: TRUE 10.94/4.19 f728_out(x228, x229) -> f718_out(x228, x229) :|: TRUE 10.94/4.19 f718_in(x230, x231) -> f727_in(x230, x231) :|: TRUE 10.94/4.19 f727_out(x232, x233) -> f718_out(x232, x233) :|: TRUE 10.94/4.19 f728_in(s(s(T73)), T74) -> f736_in(T73, T74) :|: TRUE 10.94/4.19 f736_out(x234, x235) -> f728_out(s(s(x234)), x235) :|: TRUE 10.94/4.19 f738_out -> f728_out(x236, x237) :|: TRUE 10.94/4.19 f728_in(x238, x239) -> f738_in :|: TRUE 10.94/4.19 f740_out(x240, x241) -> f736_out(x242, x241) :|: TRUE 10.94/4.19 f736_in(x243, x244) -> f739_in(x243) :|: TRUE 10.94/4.19 f739_out(x245) -> f740_in(x246, x247) :|: TRUE 10.94/4.19 f741_out(x248, x249) -> f740_out(x248, x249) :|: TRUE 10.94/4.19 f740_in(x250, x251) -> f741_in(x250, x251) :|: TRUE 10.94/4.19 f742_out(x252, x253) -> f741_out(x252, x253) :|: TRUE 10.94/4.19 f743_out(x254, x255) -> f741_out(x254, x255) :|: TRUE 10.94/4.19 f741_in(x256, x257) -> f742_in(x256, x257) :|: TRUE 10.94/4.19 f741_in(x258, x259) -> f743_in(x258, x259) :|: TRUE 10.94/4.19 f743_in(x260, x261) -> f748_in(x260, x261) :|: TRUE 10.94/4.19 f743_in(x262, x263) -> f747_in(x262, x263) :|: TRUE 10.94/4.19 f747_out(x264, x265) -> f743_out(x264, x265) :|: TRUE 10.94/4.19 f748_out(x266, x267) -> f743_out(x266, x267) :|: TRUE 10.94/4.19 f748_in(x268, x269) -> f879_in :|: TRUE 10.94/4.19 f748_in(s(s(T80)), T81) -> f878_in(T80, T81) :|: TRUE 10.94/4.19 f878_out(x270, x271) -> f748_out(s(s(x270)), x271) :|: TRUE 10.94/4.19 f879_out -> f748_out(x272, x273) :|: TRUE 10.94/4.19 f881_out(x274, s(s(s(s(s(s(s(0))))))), x275) -> f878_out(x274, x275) :|: TRUE 10.94/4.19 f878_in(x276, x277) -> f881_in(x276, s(s(s(s(s(s(s(0))))))), x277) :|: TRUE 10.94/4.19 f883_out(x278, x279, x280) -> f881_out(x281, x279, x280) :|: TRUE 10.94/4.19 f882_out(x282) -> f883_in(x283, x284, x285) :|: TRUE 10.94/4.19 f881_in(x286, x287, x288) -> f882_in(x286) :|: TRUE 10.94/4.19 f882_in(x289) -> f409_in(x289) :|: TRUE 10.94/4.19 f409_out(x290) -> f882_out(x290) :|: TRUE 10.94/4.19 f409_out(x291) -> f710_out(x291) :|: TRUE 10.94/4.19 f710_in(x292) -> f409_in(x292) :|: TRUE 10.94/4.19 f536_in(x293) -> f409_in(x293) :|: TRUE 10.94/4.19 f409_out(x294) -> f536_out(x294) :|: TRUE 10.94/4.19 f739_in(x295) -> f409_in(x295) :|: TRUE 10.94/4.19 f409_out(x296) -> f739_out(x296) :|: TRUE 10.94/4.19 f556_in(x297) -> f409_in(x297) :|: TRUE 10.94/4.19 f409_out(x298) -> f556_out(x298) :|: TRUE 10.94/4.19 Start term: f20_in(T2) 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (106) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 10.94/4.19 Constructed simple dependency graph. 10.94/4.19 10.94/4.19 Simplified to the following IRSwTs: 10.94/4.19 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (107) 10.94/4.19 TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (108) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f484_in(T37) -> f489_in :|: TRUE 10.94/4.19 f488_out -> f484_out(0) :|: TRUE 10.94/4.19 f484_in(0) -> f488_in :|: TRUE 10.94/4.19 f489_out -> f484_out(x) :|: TRUE 10.94/4.19 f494_in -> f494_out :|: TRUE 10.94/4.19 f883_out(T83, T82, T81) -> f881_out(T80, T82, T81) :|: TRUE 10.94/4.19 f882_out(x1) -> f883_in(x2, x3, x4) :|: TRUE 10.94/4.19 f881_in(x5, x6, x7) -> f882_in(x5) :|: TRUE 10.94/4.19 f474_out(T32) -> f473_out(T32) :|: TRUE 10.94/4.19 f473_in(x8) -> f474_in(x8) :|: TRUE 10.94/4.19 f485_in(x9) -> f492_in(x9) :|: TRUE 10.94/4.19 f492_out(x10) -> f485_out(x10) :|: TRUE 10.94/4.19 f491_out(x11) -> f485_out(x11) :|: TRUE 10.94/4.19 f485_in(x12) -> f491_in(x12) :|: TRUE 10.94/4.19 f480_out(x13) -> f474_out(x13) :|: TRUE 10.94/4.19 f474_in(x14) -> f480_in(x14) :|: TRUE 10.94/4.19 f882_in(x15) -> f409_in(x15) :|: TRUE 10.94/4.19 f409_out(x16) -> f882_out(x16) :|: TRUE 10.94/4.19 f488_in -> f488_out :|: TRUE 10.94/4.19 f927_in(s(s(T102)), T103, T104) -> f931_in(T102, T103, T104) :|: TRUE 10.94/4.19 f932_out -> f927_out(x17, x18, x19) :|: TRUE 10.94/4.19 f927_in(x20, x21, x22) -> f932_in :|: TRUE 10.94/4.19 f931_out(x23, x24, x25) -> f927_out(s(s(x23)), x24, x25) :|: TRUE 10.94/4.19 f483_in(x26) -> f484_in(x26) :|: TRUE 10.94/4.19 f484_out(x27) -> f483_out(x27) :|: TRUE 10.94/4.19 f483_in(x28) -> f485_in(x28) :|: TRUE 10.94/4.19 f485_out(x29) -> f483_out(x29) :|: TRUE 10.94/4.19 f480_in(x30) -> f483_in(x30) :|: TRUE 10.94/4.19 f483_out(x31) -> f480_out(x31) :|: TRUE 10.94/4.19 f884_out(x32, x33, x34) -> f883_out(x32, x33, x34) :|: TRUE 10.94/4.19 f883_in(x35, x36, x37) -> f884_in(x35, x36, x37) :|: TRUE 10.94/4.19 f931_in(x38, x39, x40) -> f881_in(x38, s(x39), x40) :|: TRUE 10.94/4.19 f881_out(x41, s(x42), x43) -> f931_out(x41, x42, x43) :|: TRUE 10.94/4.19 f473_out(x44) -> f472_out(x44) :|: TRUE 10.94/4.19 f472_in(x45) -> f473_in(x45) :|: TRUE 10.94/4.19 f884_in(x46, x47, x48) -> f886_in(x46, x47, x48) :|: TRUE 10.94/4.19 f886_out(x49, x50, x51) -> f884_out(x49, x50, x51) :|: TRUE 10.94/4.19 f885_out(x52, x53, x54) -> f884_out(x52, x53, x54) :|: TRUE 10.94/4.19 f884_in(x55, x56, x57) -> f885_in(x55, x56, x57) :|: TRUE 10.94/4.19 f927_out(x58, x59, x60) -> f886_out(x58, x59, x60) :|: TRUE 10.94/4.19 f886_in(x61, x62, x63) -> f926_in(x61, x62, x63) :|: TRUE 10.94/4.19 f926_out(x64, x65, x66) -> f886_out(x64, x65, x66) :|: TRUE 10.94/4.19 f886_in(x67, x68, x69) -> f927_in(x67, x68, x69) :|: TRUE 10.94/4.19 f491_in(s(0)) -> f494_in :|: TRUE 10.94/4.19 f491_in(x70) -> f496_in :|: TRUE 10.94/4.19 f496_out -> f491_out(x71) :|: TRUE 10.94/4.19 f494_out -> f491_out(s(0)) :|: TRUE 10.94/4.19 f480_out(T40) -> f499_out(T40) :|: TRUE 10.94/4.19 f499_in(x72) -> f480_in(x72) :|: TRUE 10.94/4.19 f409_in(x73) -> f472_in(x73) :|: TRUE 10.94/4.19 f472_out(x74) -> f409_out(x74) :|: TRUE 10.94/4.19 f492_in(x75) -> f500_in :|: TRUE 10.94/4.19 f492_in(s(s(x76))) -> f499_in(x76) :|: TRUE 10.94/4.19 f500_out -> f492_out(x77) :|: TRUE 10.94/4.19 f499_out(x78) -> f492_out(s(s(x78))) :|: TRUE 10.94/4.19 f20_in(T2) -> f21_in(T2) :|: TRUE 10.94/4.19 f21_out(x79) -> f20_out(x79) :|: TRUE 10.94/4.19 f172_out(T9) -> f21_out(T9) :|: TRUE 10.94/4.19 f21_in(x80) -> f172_in(x80) :|: TRUE 10.94/4.19 f172_in(x81) -> f176_in(x81) :|: TRUE 10.94/4.19 f176_out(x82) -> f172_out(x82) :|: TRUE 10.94/4.19 f182_out(x83) -> f176_out(x83) :|: TRUE 10.94/4.19 f180_out(x84) -> f176_out(x84) :|: TRUE 10.94/4.19 f176_in(x85) -> f182_in(x85) :|: TRUE 10.94/4.19 f176_in(x86) -> f180_in(x86) :|: TRUE 10.94/4.19 f182_in(x87) -> f233_in(x87) :|: TRUE 10.94/4.19 f234_out(x88) -> f182_out(x88) :|: TRUE 10.94/4.19 f233_out(x89) -> f182_out(x89) :|: TRUE 10.94/4.19 f182_in(x90) -> f234_in(x90) :|: TRUE 10.94/4.19 f239_out -> f234_out(x91) :|: TRUE 10.94/4.19 f238_out(T16) -> f234_out(T16) :|: TRUE 10.94/4.19 f234_in(x92) -> f239_in :|: TRUE 10.94/4.19 f234_in(x93) -> f238_in(x93) :|: TRUE 10.94/4.19 f238_in(x94) -> f243_in :|: TRUE 10.94/4.19 f243_out -> f244_in(x95, x96) :|: TRUE 10.94/4.19 f244_out(x97, x98) -> f238_out(x98) :|: TRUE 10.94/4.19 f280_out(x99, x100) -> f244_out(x99, x100) :|: TRUE 10.94/4.19 f244_in(x101, x102) -> f280_in(x101, x102) :|: TRUE 10.94/4.19 f280_in(x103, x104) -> f281_in(x103, x104) :|: TRUE 10.94/4.19 f281_out(x105, x106) -> f280_out(x105, x106) :|: TRUE 10.94/4.19 f282_out(x107, x108) -> f280_out(x107, x108) :|: TRUE 10.94/4.19 f280_in(x109, x110) -> f282_in(x109, x110) :|: TRUE 10.94/4.19 f398_out(x111, x112) -> f282_out(x111, x112) :|: TRUE 10.94/4.19 f282_in(x113, x114) -> f398_in(x113, x114) :|: TRUE 10.94/4.19 f399_out(x115, x116) -> f282_out(x115, x116) :|: TRUE 10.94/4.19 f282_in(x117, x118) -> f399_in(x117, x118) :|: TRUE 10.94/4.19 f399_in(x119, x120) -> f408_in :|: TRUE 10.94/4.19 f408_out -> f399_out(x121, x122) :|: TRUE 10.94/4.19 f399_in(s(s(x123)), x124) -> f405_in(x123, x124) :|: TRUE 10.94/4.19 f405_out(x125, x126) -> f399_out(s(s(x125)), x126) :|: TRUE 10.94/4.19 f405_in(x127, x128) -> f409_in(x127) :|: TRUE 10.94/4.19 f410_out(x129, x130) -> f405_out(x131, x130) :|: TRUE 10.94/4.19 f409_out(x132) -> f410_in(x133, x134) :|: TRUE 10.94/4.19 f510_out(T34, T33) -> f410_out(T34, T33) :|: TRUE 10.94/4.19 f410_in(x135, x136) -> f510_in(x135, x136) :|: TRUE 10.94/4.19 f515_out(x137, x138) -> f510_out(x137, x138) :|: TRUE 10.94/4.19 f510_in(x139, x140) -> f515_in(x139, x140) :|: TRUE 10.94/4.19 f510_in(x141, x142) -> f513_in(x141, x142) :|: TRUE 10.94/4.19 f513_out(x143, x144) -> f510_out(x143, x144) :|: TRUE 10.94/4.19 f515_in(x145, x146) -> f522_in(x145, x146) :|: TRUE 10.94/4.19 f522_out(x147, x148) -> f515_out(x147, x148) :|: TRUE 10.94/4.19 f515_in(x149, x150) -> f521_in(x149, x150) :|: TRUE 10.94/4.19 f521_out(x151, x152) -> f515_out(x151, x152) :|: TRUE 10.94/4.19 f530_out -> f522_out(x153, x154) :|: TRUE 10.94/4.19 f529_out(T45, T46) -> f522_out(s(s(T45)), T46) :|: TRUE 10.94/4.19 f522_in(x155, x156) -> f530_in :|: TRUE 10.94/4.19 f522_in(s(s(x157)), x158) -> f529_in(x157, x158) :|: TRUE 10.94/4.19 f537_out(x159, x160) -> f529_out(x161, x160) :|: TRUE 10.94/4.19 f536_out(x162) -> f537_in(x163, x164) :|: TRUE 10.94/4.19 f529_in(x165, x166) -> f536_in(x165) :|: TRUE 10.94/4.19 f542_out(x167, x168) -> f537_out(x167, x168) :|: TRUE 10.94/4.19 f537_in(x169, x170) -> f542_in(x169, x170) :|: TRUE 10.94/4.19 f542_in(x171, x172) -> f544_in(x171, x172) :|: TRUE 10.94/4.19 f542_in(x173, x174) -> f545_in(x173, x174) :|: TRUE 10.94/4.19 f544_out(x175, x176) -> f542_out(x175, x176) :|: TRUE 10.94/4.19 f545_out(x177, x178) -> f542_out(x177, x178) :|: TRUE 10.94/4.19 f545_in(x179, x180) -> f550_in(x179, x180) :|: TRUE 10.94/4.19 f550_out(x181, x182) -> f545_out(x181, x182) :|: TRUE 10.94/4.19 f549_out(x183, x184) -> f545_out(x183, x184) :|: TRUE 10.94/4.19 f545_in(x185, x186) -> f549_in(x185, x186) :|: TRUE 10.94/4.19 f555_out -> f550_out(x187, x188) :|: TRUE 10.94/4.19 f550_in(s(s(T52)), T53) -> f554_in(T52, T53) :|: TRUE 10.94/4.19 f554_out(x189, x190) -> f550_out(s(s(x189)), x190) :|: TRUE 10.94/4.19 f550_in(x191, x192) -> f555_in :|: TRUE 10.94/4.19 f556_out(x193) -> f557_in(x194, x195) :|: TRUE 10.94/4.19 f557_out(x196, x197) -> f554_out(x198, x197) :|: TRUE 10.94/4.19 f554_in(x199, x200) -> f556_in(x199) :|: TRUE 10.94/4.19 f557_in(x201, x202) -> f558_in(x201, x202) :|: TRUE 10.94/4.19 f558_out(x203, x204) -> f557_out(x203, x204) :|: TRUE 10.94/4.19 f558_in(x205, x206) -> f559_in(x205, x206) :|: TRUE 10.94/4.19 f559_out(x207, x208) -> f558_out(x207, x208) :|: TRUE 10.94/4.19 f560_out(x209, x210) -> f558_out(x209, x210) :|: TRUE 10.94/4.19 f558_in(x211, x212) -> f560_in(x211, x212) :|: TRUE 10.94/4.19 f560_in(x213, x214) -> f565_in(x213, x214) :|: TRUE 10.94/4.19 f564_out(x215, x216) -> f560_out(x215, x216) :|: TRUE 10.94/4.19 f560_in(x217, x218) -> f564_in(x217, x218) :|: TRUE 10.94/4.19 f565_out(x219, x220) -> f560_out(x219, x220) :|: TRUE 10.94/4.19 f679_out(T59, T60) -> f565_out(s(s(T59)), T60) :|: TRUE 10.94/4.19 f680_out -> f565_out(x221, x222) :|: TRUE 10.94/4.19 f565_in(x223, x224) -> f680_in :|: TRUE 10.94/4.19 f565_in(s(s(x225)), x226) -> f679_in(x225, x226) :|: TRUE 10.94/4.19 f679_in(x227, x228) -> f686_in(x227) :|: TRUE 10.94/4.19 f687_out(x229, x230) -> f679_out(x231, x230) :|: TRUE 10.94/4.19 f686_out(x232) -> f687_in(x233, x234) :|: TRUE 10.94/4.19 f687_in(x235, x236) -> f690_in(x235, x236) :|: TRUE 10.94/4.19 f690_out(x237, x238) -> f687_out(x237, x238) :|: TRUE 10.94/4.19 f690_in(x239, x240) -> f693_in(x239, x240) :|: TRUE 10.94/4.19 f691_out(x241, x242) -> f690_out(x241, x242) :|: TRUE 10.94/4.19 f693_out(x243, x244) -> f690_out(x243, x244) :|: TRUE 10.94/4.19 f690_in(x245, x246) -> f691_in(x245, x246) :|: TRUE 10.94/4.19 f693_in(x247, x248) -> f699_in(x247, x248) :|: TRUE 10.94/4.19 f699_out(x249, x250) -> f693_out(x249, x250) :|: TRUE 10.94/4.19 f700_out(x251, x252) -> f693_out(x251, x252) :|: TRUE 10.94/4.19 f693_in(x253, x254) -> f700_in(x253, x254) :|: TRUE 10.94/4.19 f700_in(s(s(T66)), T67) -> f707_in(T66, T67) :|: TRUE 10.94/4.19 f707_out(x255, x256) -> f700_out(s(s(x255)), x256) :|: TRUE 10.94/4.19 f700_in(x257, x258) -> f708_in :|: TRUE 10.94/4.19 f708_out -> f700_out(x259, x260) :|: TRUE 10.94/4.19 f712_out(x261, x262) -> f707_out(x263, x262) :|: TRUE 10.94/4.19 f710_out(x264) -> f712_in(x265, x266) :|: TRUE 10.94/4.19 f707_in(x267, x268) -> f710_in(x267) :|: TRUE 10.94/4.19 f712_in(x269, x270) -> f716_in(x269, x270) :|: TRUE 10.94/4.19 f716_out(x271, x272) -> f712_out(x271, x272) :|: TRUE 10.94/4.19 f716_in(x273, x274) -> f717_in(x273, x274) :|: TRUE 10.94/4.19 f717_out(x275, x276) -> f716_out(x275, x276) :|: TRUE 10.94/4.19 f716_in(x277, x278) -> f718_in(x277, x278) :|: TRUE 10.94/4.19 f718_out(x279, x280) -> f716_out(x279, x280) :|: TRUE 10.94/4.19 f718_in(x281, x282) -> f728_in(x281, x282) :|: TRUE 10.94/4.19 f728_out(x283, x284) -> f718_out(x283, x284) :|: TRUE 10.94/4.19 f718_in(x285, x286) -> f727_in(x285, x286) :|: TRUE 10.94/4.19 f727_out(x287, x288) -> f718_out(x287, x288) :|: TRUE 10.94/4.19 f728_in(s(s(T73)), T74) -> f736_in(T73, T74) :|: TRUE 10.94/4.19 f736_out(x289, x290) -> f728_out(s(s(x289)), x290) :|: TRUE 10.94/4.19 f738_out -> f728_out(x291, x292) :|: TRUE 10.94/4.19 f728_in(x293, x294) -> f738_in :|: TRUE 10.94/4.19 f740_out(x295, x296) -> f736_out(x297, x296) :|: TRUE 10.94/4.19 f736_in(x298, x299) -> f739_in(x298) :|: TRUE 10.94/4.19 f739_out(x300) -> f740_in(x301, x302) :|: TRUE 10.94/4.19 f741_out(x303, x304) -> f740_out(x303, x304) :|: TRUE 10.94/4.19 f740_in(x305, x306) -> f741_in(x305, x306) :|: TRUE 10.94/4.19 f742_out(x307, x308) -> f741_out(x307, x308) :|: TRUE 10.94/4.19 f743_out(x309, x310) -> f741_out(x309, x310) :|: TRUE 10.94/4.19 f741_in(x311, x312) -> f742_in(x311, x312) :|: TRUE 10.94/4.19 f741_in(x313, x314) -> f743_in(x313, x314) :|: TRUE 10.94/4.19 f743_in(x315, x316) -> f748_in(x315, x316) :|: TRUE 10.94/4.19 f743_in(x317, x318) -> f747_in(x317, x318) :|: TRUE 10.94/4.19 f747_out(x319, x320) -> f743_out(x319, x320) :|: TRUE 10.94/4.19 f748_out(x321, x322) -> f743_out(x321, x322) :|: TRUE 10.94/4.19 f748_in(x323, x324) -> f879_in :|: TRUE 10.94/4.19 f748_in(s(s(x325)), x326) -> f878_in(x325, x326) :|: TRUE 10.94/4.19 f878_out(x327, x328) -> f748_out(s(s(x327)), x328) :|: TRUE 10.94/4.19 f879_out -> f748_out(x329, x330) :|: TRUE 10.94/4.19 f881_out(x331, s(s(s(s(s(s(s(0))))))), x332) -> f878_out(x331, x332) :|: TRUE 10.94/4.19 f878_in(x333, x334) -> f881_in(x333, s(s(s(s(s(s(s(0))))))), x334) :|: TRUE 10.94/4.19 Start term: f20_in(T2) 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (109) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 10.94/4.19 Constructed simple dependency graph. 10.94/4.19 10.94/4.19 Simplified to the following IRSwTs: 10.94/4.19 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (110) 10.94/4.19 TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (111) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f278_out -> f274_out :|: TRUE 10.94/4.19 f274_in -> f278_in :|: TRUE 10.94/4.19 f274_in -> f279_in :|: TRUE 10.94/4.19 f279_out -> f274_out :|: TRUE 10.94/4.19 f266_in -> f267_in :|: TRUE 10.94/4.19 f267_out -> f266_out :|: TRUE 10.94/4.19 f269_in -> f273_in :|: TRUE 10.94/4.19 f273_out -> f269_out :|: TRUE 10.94/4.19 f274_out -> f269_out :|: TRUE 10.94/4.19 f269_in -> f274_in :|: TRUE 10.94/4.19 f266_out -> f278_out :|: TRUE 10.94/4.19 f278_in -> f266_in :|: TRUE 10.94/4.19 f267_in -> f268_in :|: TRUE 10.94/4.19 f268_out -> f267_out :|: TRUE 10.94/4.19 f267_in -> f269_in :|: TRUE 10.94/4.19 f269_out -> f267_out :|: TRUE 10.94/4.19 f20_in(T2) -> f21_in(T2) :|: TRUE 10.94/4.19 f21_out(x) -> f20_out(x) :|: TRUE 10.94/4.19 f172_out(T9) -> f21_out(T9) :|: TRUE 10.94/4.19 f21_in(x1) -> f172_in(x1) :|: TRUE 10.94/4.19 f172_in(x2) -> f176_in(x2) :|: TRUE 10.94/4.19 f176_out(x3) -> f172_out(x3) :|: TRUE 10.94/4.19 f182_out(x4) -> f176_out(x4) :|: TRUE 10.94/4.19 f180_out(x5) -> f176_out(x5) :|: TRUE 10.94/4.19 f176_in(x6) -> f182_in(x6) :|: TRUE 10.94/4.19 f176_in(x7) -> f180_in(x7) :|: TRUE 10.94/4.19 f182_in(x8) -> f233_in(x8) :|: TRUE 10.94/4.19 f234_out(x9) -> f182_out(x9) :|: TRUE 10.94/4.19 f233_out(x10) -> f182_out(x10) :|: TRUE 10.94/4.19 f182_in(x11) -> f234_in(x11) :|: TRUE 10.94/4.19 f239_out -> f234_out(x12) :|: TRUE 10.94/4.19 f238_out(T16) -> f234_out(T16) :|: TRUE 10.94/4.19 f234_in(x13) -> f239_in :|: TRUE 10.94/4.19 f234_in(x14) -> f238_in(x14) :|: TRUE 10.94/4.19 f238_in(x15) -> f243_in :|: TRUE 10.94/4.19 f243_out -> f244_in(x16, x17) :|: TRUE 10.94/4.19 f244_out(x18, x19) -> f238_out(x19) :|: TRUE 10.94/4.19 f243_in -> f249_in :|: TRUE 10.94/4.19 f249_out -> f243_out :|: TRUE 10.94/4.19 f249_in -> f250_in :|: TRUE 10.94/4.19 f250_out -> f249_out :|: TRUE 10.94/4.19 f250_in -> f251_in :|: TRUE 10.94/4.19 f251_out -> f250_out :|: TRUE 10.94/4.19 f251_in -> f266_in :|: TRUE 10.94/4.19 f266_out -> f251_out :|: TRUE 10.94/4.19 Start term: f20_in(T2) 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (112) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 10.94/4.19 Constructed simple dependency graph. 10.94/4.19 10.94/4.19 Simplified to the following IRSwTs: 10.94/4.19 10.94/4.19 intTRSProblem: 10.94/4.19 f274_in -> f278_in :|: TRUE 10.94/4.19 f266_in -> f267_in :|: TRUE 10.94/4.19 f269_in -> f274_in :|: TRUE 10.94/4.19 f278_in -> f266_in :|: TRUE 10.94/4.19 f267_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (113) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f274_in -> f278_in :|: TRUE 10.94/4.19 f266_in -> f267_in :|: TRUE 10.94/4.19 f269_in -> f274_in :|: TRUE 10.94/4.19 f278_in -> f266_in :|: TRUE 10.94/4.19 f267_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (114) IntTRSCompressionProof (EQUIVALENT) 10.94/4.19 Compressed rules. 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (115) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f269_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (116) IRSFormatTransformerProof (EQUIVALENT) 10.94/4.19 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (117) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f269_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (118) IRSwTTerminationDigraphProof (EQUIVALENT) 10.94/4.19 Constructed termination digraph! 10.94/4.19 Nodes: 10.94/4.19 (1) f269_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 Arcs: 10.94/4.19 (1) -> (1) 10.94/4.19 10.94/4.19 This digraph is fully evaluated! 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (119) 10.94/4.19 Obligation: 10.94/4.19 10.94/4.19 Termination digraph: 10.94/4.19 Nodes: 10.94/4.19 (1) f269_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 Arcs: 10.94/4.19 (1) -> (1) 10.94/4.19 10.94/4.19 This digraph is fully evaluated! 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (120) FilterProof (EQUIVALENT) 10.94/4.19 Used the following sort dictionary for filtering: 10.94/4.19 f269_in() 10.94/4.19 Replaced non-predefined constructor symbols by 0. 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (121) 10.94/4.19 Obligation: 10.94/4.19 Rules: 10.94/4.19 f269_in -> f269_in :|: TRUE 10.94/4.19 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (122) IntTRSPeriodicNontermProof (COMPLETE) 10.94/4.19 Normalized system to the following form: 10.94/4.19 f(pc) -> f(1) :|: pc = 1 && TRUE 10.94/4.19 Witness term starting non-terminating reduction: f(1) 10.94/4.19 ---------------------------------------- 10.94/4.19 10.94/4.19 (123) 10.94/4.19 NO 10.94/4.22 EOF