24.42/7.19 MAYBE 24.42/7.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 24.42/7.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.42/7.21 24.42/7.21 24.42/7.21 Left Termination of the query pattern 24.42/7.21 24.42/7.21 ms(a,g) 24.42/7.21 24.42/7.21 w.r.t. the given Prolog program could not be shown: 24.42/7.21 24.42/7.21 (0) Prolog 24.42/7.21 (1) PrologToPiTRSProof [SOUND, 0 ms] 24.42/7.21 (2) PiTRS 24.42/7.21 (3) DependencyPairsProof [EQUIVALENT, 57 ms] 24.42/7.21 (4) PiDP 24.42/7.21 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (6) AND 24.42/7.21 (7) PiDP 24.42/7.21 (8) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (9) PiDP 24.42/7.21 (10) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (11) QDP 24.42/7.21 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (13) YES 24.42/7.21 (14) PiDP 24.42/7.21 (15) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (16) PiDP 24.42/7.21 (17) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (18) QDP 24.42/7.21 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (20) YES 24.42/7.21 (21) PiDP 24.42/7.21 (22) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (23) PiDP 24.42/7.21 (24) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (25) QDP 24.42/7.21 (26) NonTerminationLoopProof [COMPLETE, 0 ms] 24.42/7.21 (27) NO 24.42/7.21 (28) PiDP 24.42/7.21 (29) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (30) PiDP 24.42/7.21 (31) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (32) QDP 24.42/7.21 (33) TransformationProof [SOUND, 0 ms] 24.42/7.21 (34) QDP 24.42/7.21 (35) TransformationProof [SOUND, 0 ms] 24.42/7.21 (36) QDP 24.42/7.21 (37) PiDP 24.42/7.21 (38) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (39) PiDP 24.42/7.21 (40) PiDP 24.42/7.21 (41) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (42) PiDP 24.42/7.21 (43) PrologToPiTRSProof [SOUND, 0 ms] 24.42/7.21 (44) PiTRS 24.42/7.21 (45) DependencyPairsProof [EQUIVALENT, 27 ms] 24.42/7.21 (46) PiDP 24.42/7.21 (47) DependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (48) AND 24.42/7.21 (49) PiDP 24.42/7.21 (50) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (51) PiDP 24.42/7.21 (52) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (53) QDP 24.42/7.21 (54) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (55) YES 24.42/7.21 (56) PiDP 24.42/7.21 (57) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (58) PiDP 24.42/7.21 (59) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (60) QDP 24.42/7.21 (61) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (62) YES 24.42/7.21 (63) PiDP 24.42/7.21 (64) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (65) PiDP 24.42/7.21 (66) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (67) QDP 24.42/7.21 (68) NonTerminationLoopProof [COMPLETE, 0 ms] 24.42/7.21 (69) NO 24.42/7.21 (70) PiDP 24.42/7.21 (71) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (72) PiDP 24.42/7.21 (73) PiDPToQDPProof [SOUND, 1 ms] 24.42/7.21 (74) QDP 24.42/7.21 (75) TransformationProof [SOUND, 0 ms] 24.42/7.21 (76) QDP 24.42/7.21 (77) TransformationProof [SOUND, 0 ms] 24.42/7.21 (78) QDP 24.42/7.21 (79) PiDP 24.42/7.21 (80) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (81) PiDP 24.42/7.21 (82) PiDP 24.42/7.21 (83) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (84) PiDP 24.42/7.21 (85) PrologToTRSTransformerProof [SOUND, 48 ms] 24.42/7.21 (86) QTRS 24.42/7.21 (87) DependencyPairsProof [EQUIVALENT, 2 ms] 24.42/7.21 (88) QDP 24.42/7.21 (89) DependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (90) AND 24.42/7.21 (91) QDP 24.42/7.21 (92) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (93) QDP 24.42/7.21 (94) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (95) YES 24.42/7.21 (96) QDP 24.42/7.21 (97) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (98) YES 24.42/7.21 (99) QDP 24.42/7.21 (100) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (101) QDP 24.42/7.21 (102) NonTerminationLoopProof [COMPLETE, 0 ms] 24.42/7.21 (103) NO 24.42/7.21 (104) QDP 24.42/7.21 (105) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (106) QDP 24.42/7.21 (107) QDP 24.42/7.21 (108) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (109) QDP 24.42/7.21 (110) NonTerminationLoopProof [COMPLETE, 0 ms] 24.42/7.21 (111) NO 24.42/7.21 (112) QDP 24.42/7.21 (113) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (114) QDP 24.42/7.21 (115) PrologToDTProblemTransformerProof [SOUND, 171 ms] 24.42/7.21 (116) TRIPLES 24.42/7.21 (117) UndefinedPredicateInTriplesTransformerProof [SOUND, 0 ms] 24.42/7.21 (118) TRIPLES 24.42/7.21 (119) TriplesToPiDPProof [SOUND, 152 ms] 24.42/7.21 (120) PiDP 24.42/7.21 (121) DependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (122) AND 24.42/7.21 (123) PiDP 24.42/7.21 (124) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (125) PiDP 24.42/7.21 (126) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (127) QDP 24.42/7.21 (128) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (129) YES 24.42/7.21 (130) PiDP 24.42/7.21 (131) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (132) PiDP 24.42/7.21 (133) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (134) QDP 24.42/7.21 (135) QDPSizeChangeProof [EQUIVALENT, 0 ms] 24.42/7.21 (136) YES 24.42/7.21 (137) PiDP 24.42/7.21 (138) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (139) PiDP 24.42/7.21 (140) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (141) QDP 24.42/7.21 (142) NonTerminationLoopProof [COMPLETE, 0 ms] 24.42/7.21 (143) NO 24.42/7.21 (144) PiDP 24.42/7.21 (145) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (146) PiDP 24.42/7.21 (147) PiDPToQDPProof [SOUND, 0 ms] 24.42/7.21 (148) QDP 24.42/7.21 (149) PiDP 24.42/7.21 (150) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (151) PiDP 24.42/7.21 (152) PiDP 24.42/7.21 (153) UsableRulesProof [EQUIVALENT, 0 ms] 24.42/7.21 (154) PiDP 24.42/7.21 (155) PrologToIRSwTTransformerProof [SOUND, 129 ms] 24.42/7.21 (156) AND 24.42/7.21 (157) IRSwT 24.42/7.21 (158) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (159) TRUE 24.42/7.21 (160) IRSwT 24.42/7.21 (161) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (162) TRUE 24.42/7.21 (163) IRSwT 24.42/7.21 (164) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (165) TRUE 24.42/7.21 (166) IRSwT 24.42/7.21 (167) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (168) TRUE 24.42/7.21 (169) IRSwT 24.42/7.21 (170) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (171) IRSwT 24.42/7.21 (172) IntTRSCompressionProof [EQUIVALENT, 20 ms] 24.42/7.21 (173) IRSwT 24.42/7.21 (174) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 24.42/7.21 (175) IRSwT 24.42/7.21 (176) IRSwTTerminationDigraphProof [EQUIVALENT, 8 ms] 24.42/7.21 (177) IRSwT 24.42/7.21 (178) FilterProof [EQUIVALENT, 0 ms] 24.42/7.21 (179) IntTRS 24.42/7.21 (180) IntTRSNonPeriodicNontermProof [COMPLETE, 2 ms] 24.42/7.21 (181) NO 24.42/7.21 (182) IRSwT 24.42/7.21 (183) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 24.42/7.21 (184) IRSwT 24.42/7.21 (185) IntTRSCompressionProof [EQUIVALENT, 12 ms] 24.42/7.21 (186) IRSwT 24.42/7.21 (187) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 24.42/7.21 (188) IRSwT 24.42/7.21 (189) IRSwTTerminationDigraphProof [EQUIVALENT, 10 ms] 24.42/7.21 (190) IRSwT 24.42/7.21 (191) FilterProof [EQUIVALENT, 0 ms] 24.42/7.21 (192) IntTRS 24.42/7.21 (193) IntTRSPeriodicNontermProof [COMPLETE, 9 ms] 24.42/7.21 (194) NO 24.42/7.21 24.42/7.21 24.42/7.21 ---------------------------------------- 24.42/7.21 24.42/7.21 (0) 24.42/7.21 Obligation: 24.42/7.21 Clauses: 24.42/7.21 24.42/7.21 ms([], []). 24.42/7.21 ms(.(X, []), .(X, [])). 24.42/7.21 ms(.(X, .(Y, Xs)), Ys) :- ','(split(.(X, .(Y, Xs)), X1s, X2s), ','(ms(X1s, Y1s), ','(ms(X2s, Y2s), merge(Y1s, Y2s, Ys)))). 24.42/7.21 split([], [], []). 24.42/7.21 split(.(X, Xs), .(X, Ys), Zs) :- split(Xs, Zs, Ys). 24.42/7.21 merge([], Xs, Xs). 24.42/7.21 merge(Xs, [], Xs). 24.42/7.21 merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(less(X, s(Y)), merge(Xs, .(Y, Ys), Zs)). 24.42/7.21 merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(less(Y, X), merge(.(X, Xs), Ys, Zs)). 24.42/7.21 less(0, s(X1)). 24.42/7.21 less(s(X), s(Y)) :- less(X, Y). 24.42/7.21 24.42/7.21 24.42/7.21 Query: ms(a,g) 24.42/7.21 ---------------------------------------- 24.42/7.21 24.42/7.21 (1) PrologToPiTRSProof (SOUND) 24.42/7.21 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 24.42/7.21 24.42/7.21 ms_in_2: (f,b) (f,f) 24.42/7.21 24.42/7.21 split_in_3: (f,f,f) 24.42/7.21 24.42/7.21 merge_in_3: (f,f,f) (f,f,b) 24.42/7.21 24.42/7.21 less_in_2: (f,f) (b,f) 24.42/7.21 24.42/7.21 Transforming Prolog into the following Term Rewriting System: 24.42/7.21 24.42/7.21 Pi-finite rewrite system: 24.42/7.21 The TRS R consists of the following rules: 24.42/7.21 24.42/7.21 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.21 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.21 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.21 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.21 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.21 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.21 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.21 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.21 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.21 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.21 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.21 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.21 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.21 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.21 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.21 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.21 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.21 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.21 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.21 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.21 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.21 24.42/7.21 The argument filtering Pi contains the following mapping: 24.42/7.21 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.21 24.42/7.21 [] = [] 24.42/7.21 24.42/7.21 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.21 24.42/7.21 .(x1, x2) = .(x1, x2) 24.42/7.21 24.42/7.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.21 24.42/7.21 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.21 24.42/7.21 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.21 24.42/7.21 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.21 24.42/7.21 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.21 24.42/7.21 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.21 24.42/7.21 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.21 24.42/7.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.21 24.42/7.21 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.21 24.42/7.21 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.21 24.42/7.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.21 24.42/7.21 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.21 24.42/7.21 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.21 24.42/7.21 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.21 24.42/7.21 less_in_aa(x1, x2) = less_in_aa 24.42/7.21 24.42/7.21 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.21 24.42/7.21 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.21 24.42/7.21 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.21 24.42/7.21 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.21 24.42/7.21 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.21 24.42/7.21 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.21 24.42/7.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.21 24.42/7.21 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.21 24.42/7.21 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.21 24.42/7.21 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.21 24.42/7.21 0 = 0 24.42/7.21 24.42/7.21 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.21 24.42/7.21 s(x1) = s(x1) 24.42/7.21 24.42/7.21 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.21 24.42/7.21 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 24.42/7.21 24.42/7.21 24.42/7.21 24.42/7.21 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 24.42/7.21 24.42/7.21 24.42/7.21 24.42/7.21 ---------------------------------------- 24.42/7.21 24.42/7.21 (2) 24.42/7.21 Obligation: 24.42/7.21 Pi-finite rewrite system: 24.42/7.21 The TRS R consists of the following rules: 24.42/7.21 24.42/7.21 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.21 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.21 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.21 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.21 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.21 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.21 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.21 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.21 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.21 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.21 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.21 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.21 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.21 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.21 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.21 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.21 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.21 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.21 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.21 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.21 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.21 24.42/7.21 The argument filtering Pi contains the following mapping: 24.42/7.21 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.21 24.42/7.21 [] = [] 24.42/7.21 24.42/7.21 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.21 24.42/7.21 .(x1, x2) = .(x1, x2) 24.42/7.21 24.42/7.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.21 24.42/7.21 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.21 24.42/7.21 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.21 24.42/7.21 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.21 24.42/7.21 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.21 24.42/7.21 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.21 24.42/7.21 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.21 24.42/7.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.21 24.42/7.21 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.21 24.42/7.21 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.21 24.42/7.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.21 24.42/7.21 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.21 24.42/7.21 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.21 24.42/7.21 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.21 24.42/7.21 less_in_aa(x1, x2) = less_in_aa 24.42/7.21 24.42/7.21 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.21 24.42/7.21 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.21 24.42/7.21 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.21 24.42/7.21 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.21 24.42/7.21 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.21 24.42/7.21 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.21 24.42/7.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.21 24.42/7.21 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.21 24.42/7.21 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.21 24.42/7.21 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.21 24.42/7.21 0 = 0 24.42/7.21 24.42/7.21 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.21 24.42/7.21 s(x1) = s(x1) 24.42/7.21 24.42/7.21 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.21 24.42/7.21 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 24.42/7.21 24.42/7.21 ---------------------------------------- 24.42/7.21 24.42/7.21 (3) DependencyPairsProof (EQUIVALENT) 24.42/7.21 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 24.42/7.21 Pi DP problem: 24.42/7.21 The TRS P consists of the following rules: 24.42/7.21 24.42/7.21 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> U1_AG(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.42/7.21 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> U5_AAA(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.21 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.42/7.21 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AG(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.21 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.42/7.21 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.21 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AA(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.21 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AA(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.21 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAA(Y1s, Y2s, Ys) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_AA(X, s(Y)) 24.42/7.21 LESS_IN_AA(s(X), s(Y)) -> U10_AA(X, Y, less_in_aa(X, Y)) 24.42/7.21 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.42/7.21 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.21 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_AA(Y, X) 24.42/7.21 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.21 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.42/7.21 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AG(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.21 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AG(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.21 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAG(Y1s, Y2s, Ys) 24.42/7.21 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.21 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_GA(X, s(Y)) 24.42/7.21 LESS_IN_GA(s(X), s(Y)) -> U10_GA(X, Y, less_in_ga(X, Y)) 24.42/7.21 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.42/7.21 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.21 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.42/7.21 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.21 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_GA(Y, X) 24.42/7.21 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.21 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.42/7.21 24.42/7.21 The TRS R consists of the following rules: 24.42/7.21 24.42/7.21 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.21 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.21 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.21 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.21 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.21 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.21 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.21 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.21 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.21 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.21 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.21 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.21 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.21 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.21 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.21 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.21 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.21 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.21 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.21 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.21 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.21 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.21 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.21 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.21 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.21 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.21 24.42/7.21 The argument filtering Pi contains the following mapping: 24.42/7.21 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.21 24.42/7.21 [] = [] 24.42/7.21 24.42/7.21 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.21 24.42/7.21 .(x1, x2) = .(x1, x2) 24.42/7.21 24.42/7.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.21 24.42/7.21 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.21 24.42/7.21 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.21 24.42/7.21 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.21 24.42/7.21 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.21 24.42/7.21 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.21 24.42/7.21 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.21 24.42/7.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.21 24.42/7.21 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.21 24.42/7.21 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.21 24.42/7.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.21 24.42/7.21 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.21 24.42/7.21 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.21 24.42/7.21 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.21 24.42/7.21 less_in_aa(x1, x2) = less_in_aa 24.42/7.21 24.42/7.21 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.21 24.42/7.21 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.21 24.42/7.21 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.21 24.42/7.21 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.21 24.42/7.21 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.21 24.42/7.21 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.21 24.42/7.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.21 24.42/7.21 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.21 24.42/7.21 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.21 24.42/7.21 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.21 24.42/7.21 0 = 0 24.42/7.21 24.42/7.21 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.21 24.42/7.21 s(x1) = s(x1) 24.42/7.21 24.42/7.21 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.21 24.42/7.21 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.21 24.42/7.21 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.21 24.42/7.21 MS_IN_AG(x1, x2) = MS_IN_AG(x2) 24.42/7.21 24.42/7.21 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 24.42/7.21 24.42/7.21 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.42/7.21 24.42/7.21 U5_AAA(x1, x2, x3, x4, x5) = U5_AAA(x5) 24.42/7.21 24.42/7.21 U2_AG(x1, x2, x3, x4, x5, x6) = U2_AG(x4, x6) 24.42/7.21 24.42/7.21 MS_IN_AA(x1, x2) = MS_IN_AA 24.42/7.21 24.42/7.21 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.42/7.21 24.42/7.21 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.42/7.21 24.42/7.21 U3_AA(x1, x2, x3, x4, x5, x6) = U3_AA(x6) 24.42/7.21 24.42/7.21 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x5) 24.42/7.21 24.42/7.21 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.42/7.21 24.42/7.21 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.42/7.21 24.42/7.21 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.42/7.21 24.42/7.21 U10_AA(x1, x2, x3) = U10_AA(x3) 24.42/7.21 24.42/7.21 U7_AAA(x1, x2, x3, x4, x5, x6) = U7_AAA(x6) 24.42/7.21 24.42/7.21 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.42/7.21 24.42/7.21 U9_AAA(x1, x2, x3, x4, x5, x6) = U9_AAA(x6) 24.42/7.21 24.42/7.21 U3_AG(x1, x2, x3, x4, x5, x6) = U3_AG(x4, x6) 24.42/7.21 24.42/7.21 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x4, x5) 24.42/7.21 24.42/7.21 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.42/7.21 24.42/7.21 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.42/7.21 24.42/7.21 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.42/7.21 24.42/7.21 U10_GA(x1, x2, x3) = U10_GA(x1, x3) 24.42/7.21 24.42/7.21 U7_AAG(x1, x2, x3, x4, x5, x6) = U7_AAG(x1, x5, x6) 24.42/7.21 24.42/7.21 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.42/7.21 24.42/7.21 U9_AAG(x1, x2, x3, x4, x5, x6) = U9_AAG(x3, x5, x6) 24.42/7.21 24.42/7.21 24.42/7.21 We have to consider all (P,R,Pi)-chains 24.42/7.21 ---------------------------------------- 24.42/7.21 24.42/7.21 (4) 24.42/7.21 Obligation: 24.42/7.21 Pi DP problem: 24.42/7.21 The TRS P consists of the following rules: 24.42/7.21 24.42/7.21 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> U1_AG(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.42/7.21 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> U5_AAA(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.21 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.42/7.21 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AG(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.21 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.21 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.42/7.21 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.21 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.21 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AA(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.21 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.21 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AA(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.21 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAA(Y1s, Y2s, Ys) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.21 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_AA(X, s(Y)) 24.42/7.21 LESS_IN_AA(s(X), s(Y)) -> U10_AA(X, Y, less_in_aa(X, Y)) 24.42/7.22 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.42/7.22 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_AA(Y, X) 24.42/7.22 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.42/7.22 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AG(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.22 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AG(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAG(Y1s, Y2s, Ys) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_GA(X, s(Y)) 24.42/7.22 LESS_IN_GA(s(X), s(Y)) -> U10_GA(X, Y, less_in_ga(X, Y)) 24.42/7.22 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.42/7.22 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_GA(Y, X) 24.42/7.22 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 MS_IN_AG(x1, x2) = MS_IN_AG(x2) 24.42/7.22 24.42/7.22 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 24.42/7.22 24.42/7.22 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.42/7.22 24.42/7.22 U5_AAA(x1, x2, x3, x4, x5) = U5_AAA(x5) 24.42/7.22 24.42/7.22 U2_AG(x1, x2, x3, x4, x5, x6) = U2_AG(x4, x6) 24.42/7.22 24.42/7.22 MS_IN_AA(x1, x2) = MS_IN_AA 24.42/7.22 24.42/7.22 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.42/7.22 24.42/7.22 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.42/7.22 24.42/7.22 U3_AA(x1, x2, x3, x4, x5, x6) = U3_AA(x6) 24.42/7.22 24.42/7.22 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x5) 24.42/7.22 24.42/7.22 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.42/7.22 24.42/7.22 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.42/7.22 24.42/7.22 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.42/7.22 24.42/7.22 U10_AA(x1, x2, x3) = U10_AA(x3) 24.42/7.22 24.42/7.22 U7_AAA(x1, x2, x3, x4, x5, x6) = U7_AAA(x6) 24.42/7.22 24.42/7.22 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.42/7.22 24.42/7.22 U9_AAA(x1, x2, x3, x4, x5, x6) = U9_AAA(x6) 24.42/7.22 24.42/7.22 U3_AG(x1, x2, x3, x4, x5, x6) = U3_AG(x4, x6) 24.42/7.22 24.42/7.22 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x4, x5) 24.42/7.22 24.42/7.22 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.42/7.22 24.42/7.22 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.42/7.22 24.42/7.22 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.42/7.22 24.42/7.22 U10_GA(x1, x2, x3) = U10_GA(x1, x3) 24.42/7.22 24.42/7.22 U7_AAG(x1, x2, x3, x4, x5, x6) = U7_AAG(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_AAG(x1, x2, x3, x4, x5, x6) = U9_AAG(x3, x5, x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (5) DependencyGraphProof (EQUIVALENT) 24.42/7.22 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 23 less nodes. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (6) 24.42/7.22 Complex Obligation (AND) 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (7) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (8) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (9) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.42/7.22 24.42/7.22 R is empty. 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (10) PiDPToQDPProof (SOUND) 24.42/7.22 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (11) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_GA(s(X)) -> LESS_IN_GA(X) 24.42/7.22 24.42/7.22 R is empty. 24.42/7.22 Q is empty. 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (12) QDPSizeChangeProof (EQUIVALENT) 24.42/7.22 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. 24.42/7.22 24.42/7.22 From the DPs we obtained the following set of size-change graphs: 24.42/7.22 *LESS_IN_GA(s(X)) -> LESS_IN_GA(X) 24.42/7.22 The graph contains the following edges 1 > 1 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (13) 24.42/7.22 YES 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (14) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.42/7.22 24.42/7.22 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (15) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (16) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.42/7.22 24.42/7.22 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (17) PiDPToQDPProof (SOUND) 24.42/7.22 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (18) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAG(X, Zs, less_out_ga(X)) -> MERGE_IN_AAG(Zs) 24.42/7.22 MERGE_IN_AAG(.(X, Zs)) -> U6_AAG(X, Zs, less_in_ga(X)) 24.42/7.22 MERGE_IN_AAG(.(Y, Zs)) -> U8_AAG(Y, Zs, less_in_ga(Y)) 24.42/7.22 U8_AAG(Y, Zs, less_out_ga(Y)) -> MERGE_IN_AAG(Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_ga(0) -> less_out_ga(0) 24.42/7.22 less_in_ga(s(X)) -> U10_ga(X, less_in_ga(X)) 24.42/7.22 U10_ga(X, less_out_ga(X)) -> less_out_ga(s(X)) 24.42/7.22 24.42/7.22 The set Q consists of the following terms: 24.42/7.22 24.42/7.22 less_in_ga(x0) 24.42/7.22 U10_ga(x0, x1) 24.42/7.22 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (19) QDPSizeChangeProof (EQUIVALENT) 24.42/7.22 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. 24.42/7.22 24.42/7.22 From the DPs we obtained the following set of size-change graphs: 24.42/7.22 *MERGE_IN_AAG(.(X, Zs)) -> U6_AAG(X, Zs, less_in_ga(X)) 24.42/7.22 The graph contains the following edges 1 > 1, 1 > 2 24.42/7.22 24.42/7.22 24.42/7.22 *MERGE_IN_AAG(.(Y, Zs)) -> U8_AAG(Y, Zs, less_in_ga(Y)) 24.42/7.22 The graph contains the following edges 1 > 1, 1 > 2 24.42/7.22 24.42/7.22 24.42/7.22 *U6_AAG(X, Zs, less_out_ga(X)) -> MERGE_IN_AAG(Zs) 24.42/7.22 The graph contains the following edges 2 >= 1 24.42/7.22 24.42/7.22 24.42/7.22 *U8_AAG(Y, Zs, less_out_ga(Y)) -> MERGE_IN_AAG(Zs) 24.42/7.22 The graph contains the following edges 2 >= 1 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (20) 24.42/7.22 YES 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (21) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (22) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (23) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.42/7.22 24.42/7.22 R is empty. 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (24) PiDPToQDPProof (SOUND) 24.42/7.22 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (25) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 LESS_IN_AA -> LESS_IN_AA 24.42/7.22 24.42/7.22 R is empty. 24.42/7.22 Q is empty. 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (26) NonTerminationLoopProof (COMPLETE) 24.42/7.22 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 24.42/7.22 Found a loop by semiunifying a rule from P directly. 24.42/7.22 24.42/7.22 s = LESS_IN_AA evaluates to t =LESS_IN_AA 24.42/7.22 24.42/7.22 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 24.42/7.22 * Matcher: [ ] 24.42/7.22 * Semiunifier: [ ] 24.42/7.22 24.42/7.22 -------------------------------------------------------------------------------- 24.42/7.22 Rewriting sequence 24.42/7.22 24.42/7.22 The DP semiunifies directly so there is only one rewrite step from LESS_IN_AA to LESS_IN_AA. 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (27) 24.42/7.22 NO 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (28) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.42/7.22 24.42/7.22 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.42/7.22 24.42/7.22 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (29) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (30) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.42/7.22 24.42/7.22 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.42/7.22 24.42/7.22 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (31) PiDPToQDPProof (SOUND) 24.42/7.22 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (32) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.42/7.22 MERGE_IN_AAA -> U6_AAA(less_in_aa) 24.42/7.22 MERGE_IN_AAA -> U8_AAA(less_in_aa) 24.42/7.22 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_aa -> less_out_aa(0) 24.42/7.22 less_in_aa -> U10_aa(less_in_aa) 24.42/7.22 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.42/7.22 24.42/7.22 The set Q consists of the following terms: 24.42/7.22 24.42/7.22 less_in_aa 24.42/7.22 U10_aa(x0) 24.42/7.22 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (33) TransformationProof (SOUND) 24.42/7.22 By narrowing [LPAR04] the rule MERGE_IN_AAA -> U6_AAA(less_in_aa) at position [0] we obtained the following new rules [LPAR04]: 24.42/7.22 24.42/7.22 (MERGE_IN_AAA -> U6_AAA(less_out_aa(0)),MERGE_IN_AAA -> U6_AAA(less_out_aa(0))) 24.42/7.22 (MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)),MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa))) 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (34) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.42/7.22 MERGE_IN_AAA -> U8_AAA(less_in_aa) 24.42/7.22 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.42/7.22 MERGE_IN_AAA -> U6_AAA(less_out_aa(0)) 24.42/7.22 MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_aa -> less_out_aa(0) 24.42/7.22 less_in_aa -> U10_aa(less_in_aa) 24.42/7.22 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.42/7.22 24.42/7.22 The set Q consists of the following terms: 24.42/7.22 24.42/7.22 less_in_aa 24.42/7.22 U10_aa(x0) 24.42/7.22 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (35) TransformationProof (SOUND) 24.42/7.22 By narrowing [LPAR04] the rule MERGE_IN_AAA -> U8_AAA(less_in_aa) at position [0] we obtained the following new rules [LPAR04]: 24.42/7.22 24.42/7.22 (MERGE_IN_AAA -> U8_AAA(less_out_aa(0)),MERGE_IN_AAA -> U8_AAA(less_out_aa(0))) 24.42/7.22 (MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa)),MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa))) 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (36) 24.42/7.22 Obligation: 24.42/7.22 Q DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.42/7.22 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.42/7.22 MERGE_IN_AAA -> U6_AAA(less_out_aa(0)) 24.42/7.22 MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)) 24.42/7.22 MERGE_IN_AAA -> U8_AAA(less_out_aa(0)) 24.42/7.22 MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa)) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 less_in_aa -> less_out_aa(0) 24.42/7.22 less_in_aa -> U10_aa(less_in_aa) 24.42/7.22 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.42/7.22 24.42/7.22 The set Q consists of the following terms: 24.42/7.22 24.42/7.22 less_in_aa 24.42/7.22 U10_aa(x0) 24.42/7.22 24.42/7.22 We have to consider all (P,Q,R)-chains. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (37) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (38) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (39) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.42/7.22 24.42/7.22 R is empty. 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (40) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.22 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag(x2) 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x4, x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2, x3) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga(x1) 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x1, x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 MS_IN_AA(x1, x2) = MS_IN_AA 24.42/7.22 24.42/7.22 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.42/7.22 24.42/7.22 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (41) UsableRulesProof (EQUIVALENT) 24.42/7.22 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (42) 24.42/7.22 Obligation: 24.42/7.22 Pi DP problem: 24.42/7.22 The TRS P consists of the following rules: 24.42/7.22 24.42/7.22 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.42/7.22 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.42/7.22 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 MS_IN_AA(x1, x2) = MS_IN_AA 24.42/7.22 24.42/7.22 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.42/7.22 24.42/7.22 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.42/7.22 24.42/7.22 24.42/7.22 We have to consider all (P,R,Pi)-chains 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (43) PrologToPiTRSProof (SOUND) 24.42/7.22 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 24.42/7.22 24.42/7.22 ms_in_2: (f,b) (f,f) 24.42/7.22 24.42/7.22 split_in_3: (f,f,f) 24.42/7.22 24.42/7.22 merge_in_3: (f,f,f) (f,f,b) 24.42/7.22 24.42/7.22 less_in_2: (f,f) (b,f) 24.42/7.22 24.42/7.22 Transforming Prolog into the following Term Rewriting System: 24.42/7.22 24.42/7.22 Pi-finite rewrite system: 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.42/7.22 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.42/7.22 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.42/7.22 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.42/7.22 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.42/7.22 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.42/7.22 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.42/7.22 24.42/7.22 The argument filtering Pi contains the following mapping: 24.42/7.22 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.42/7.22 24.42/7.22 [] = [] 24.42/7.22 24.42/7.22 ms_out_ag(x1, x2) = ms_out_ag 24.42/7.22 24.42/7.22 .(x1, x2) = .(x1, x2) 24.42/7.22 24.42/7.22 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.42/7.22 24.42/7.22 split_in_aaa(x1, x2, x3) = split_in_aaa 24.42/7.22 24.42/7.22 split_out_aaa(x1, x2, x3) = split_out_aaa 24.42/7.22 24.42/7.22 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.42/7.22 24.42/7.22 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.42/7.22 24.42/7.22 ms_in_aa(x1, x2) = ms_in_aa 24.42/7.22 24.42/7.22 ms_out_aa(x1, x2) = ms_out_aa 24.42/7.22 24.42/7.22 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.42/7.22 24.42/7.22 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.42/7.22 24.42/7.22 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.42/7.22 24.42/7.22 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.42/7.22 24.42/7.22 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.42/7.22 24.42/7.22 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.42/7.22 24.42/7.22 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.42/7.22 24.42/7.22 less_in_aa(x1, x2) = less_in_aa 24.42/7.22 24.42/7.22 less_out_aa(x1, x2) = less_out_aa(x1) 24.42/7.22 24.42/7.22 U10_aa(x1, x2, x3) = U10_aa(x3) 24.42/7.22 24.42/7.22 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.42/7.22 24.42/7.22 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.42/7.22 24.42/7.22 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.42/7.22 24.42/7.22 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.42/7.22 24.42/7.22 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.42/7.22 24.42/7.22 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.42/7.22 24.42/7.22 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.42/7.22 24.42/7.22 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.42/7.22 24.42/7.22 less_in_ga(x1, x2) = less_in_ga(x1) 24.42/7.22 24.42/7.22 0 = 0 24.42/7.22 24.42/7.22 less_out_ga(x1, x2) = less_out_ga 24.42/7.22 24.42/7.22 s(x1) = s(x1) 24.42/7.22 24.42/7.22 U10_ga(x1, x2, x3) = U10_ga(x3) 24.42/7.22 24.42/7.22 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.42/7.22 24.42/7.22 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.42/7.22 24.42/7.22 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 24.42/7.22 24.42/7.22 24.42/7.22 24.42/7.22 ---------------------------------------- 24.42/7.22 24.42/7.22 (44) 24.42/7.22 Obligation: 24.42/7.22 Pi-finite rewrite system: 24.42/7.22 The TRS R consists of the following rules: 24.42/7.22 24.42/7.22 ms_in_ag([], []) -> ms_out_ag([], []) 24.42/7.22 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.42/7.22 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.42/7.22 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.42/7.22 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.42/7.22 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 ms_in_aa([], []) -> ms_out_aa([], []) 24.42/7.22 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.42/7.22 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.42/7.22 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.42/7.22 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.42/7.22 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.42/7.22 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.42/7.22 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.42/7.22 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.42/7.22 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.42/7.22 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.42/7.22 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.42/7.22 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.42/7.22 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.42/7.22 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.42/7.22 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.42/7.22 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.42/7.22 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.26 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.26 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.26 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.26 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.26 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.26 24.62/7.26 [] = [] 24.62/7.26 24.62/7.26 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.26 24.62/7.26 .(x1, x2) = .(x1, x2) 24.62/7.26 24.62/7.26 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.26 24.62/7.26 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.26 24.62/7.26 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.26 24.62/7.26 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.26 24.62/7.26 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.26 24.62/7.26 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.26 24.62/7.26 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.26 24.62/7.26 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.26 24.62/7.26 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.26 24.62/7.26 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.26 24.62/7.26 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.26 24.62/7.26 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.26 24.62/7.26 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.26 24.62/7.26 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.26 24.62/7.26 less_in_aa(x1, x2) = less_in_aa 24.62/7.26 24.62/7.26 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.26 24.62/7.26 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.26 24.62/7.26 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.26 24.62/7.26 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.26 24.62/7.26 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.26 24.62/7.26 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.26 24.62/7.26 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.26 24.62/7.26 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.26 24.62/7.26 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.26 24.62/7.26 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.26 24.62/7.26 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.26 24.62/7.26 0 = 0 24.62/7.26 24.62/7.26 less_out_ga(x1, x2) = less_out_ga 24.62/7.26 24.62/7.26 s(x1) = s(x1) 24.62/7.26 24.62/7.26 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.26 24.62/7.26 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.26 24.62/7.26 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.26 24.62/7.26 24.62/7.26 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (45) DependencyPairsProof (EQUIVALENT) 24.62/7.26 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 24.62/7.26 Pi DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> U1_AG(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.62/7.26 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> U5_AAA(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.62/7.26 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AG(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.26 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.62/7.26 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.26 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AA(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.26 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AA(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAA(Y1s, Y2s, Ys) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_AA(X, s(Y)) 24.62/7.26 LESS_IN_AA(s(X), s(Y)) -> U10_AA(X, Y, less_in_aa(X, Y)) 24.62/7.26 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.62/7.26 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_AA(Y, X) 24.62/7.26 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.62/7.26 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AG(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.26 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AG(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAG(Y1s, Y2s, Ys) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_GA(X, s(Y)) 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> U10_GA(X, Y, less_in_ga(X, Y)) 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.62/7.26 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_GA(Y, X) 24.62/7.26 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.62/7.26 24.62/7.26 The TRS R consists of the following rules: 24.62/7.26 24.62/7.26 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.26 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.26 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.26 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.26 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.26 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.26 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.26 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.26 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.26 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.26 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.26 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.26 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.26 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.26 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.26 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.26 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.26 24.62/7.26 [] = [] 24.62/7.26 24.62/7.26 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.26 24.62/7.26 .(x1, x2) = .(x1, x2) 24.62/7.26 24.62/7.26 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.26 24.62/7.26 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.26 24.62/7.26 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.26 24.62/7.26 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.26 24.62/7.26 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.26 24.62/7.26 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.26 24.62/7.26 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.26 24.62/7.26 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.26 24.62/7.26 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.26 24.62/7.26 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.26 24.62/7.26 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.26 24.62/7.26 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.26 24.62/7.26 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.26 24.62/7.26 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.26 24.62/7.26 less_in_aa(x1, x2) = less_in_aa 24.62/7.26 24.62/7.26 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.26 24.62/7.26 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.26 24.62/7.26 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.26 24.62/7.26 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.26 24.62/7.26 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.26 24.62/7.26 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.26 24.62/7.26 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.26 24.62/7.26 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.26 24.62/7.26 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.26 24.62/7.26 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.26 24.62/7.26 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.26 24.62/7.26 0 = 0 24.62/7.26 24.62/7.26 less_out_ga(x1, x2) = less_out_ga 24.62/7.26 24.62/7.26 s(x1) = s(x1) 24.62/7.26 24.62/7.26 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.26 24.62/7.26 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.26 24.62/7.26 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.26 24.62/7.26 MS_IN_AG(x1, x2) = MS_IN_AG(x2) 24.62/7.26 24.62/7.26 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 24.62/7.26 24.62/7.26 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.62/7.26 24.62/7.26 U5_AAA(x1, x2, x3, x4, x5) = U5_AAA(x5) 24.62/7.26 24.62/7.26 U2_AG(x1, x2, x3, x4, x5, x6) = U2_AG(x4, x6) 24.62/7.26 24.62/7.26 MS_IN_AA(x1, x2) = MS_IN_AA 24.62/7.26 24.62/7.26 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.62/7.26 24.62/7.26 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.62/7.26 24.62/7.26 U3_AA(x1, x2, x3, x4, x5, x6) = U3_AA(x6) 24.62/7.26 24.62/7.26 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x5) 24.62/7.26 24.62/7.26 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.62/7.26 24.62/7.26 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.62/7.26 24.62/7.26 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.62/7.26 24.62/7.26 U10_AA(x1, x2, x3) = U10_AA(x3) 24.62/7.26 24.62/7.26 U7_AAA(x1, x2, x3, x4, x5, x6) = U7_AAA(x6) 24.62/7.26 24.62/7.26 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.62/7.26 24.62/7.26 U9_AAA(x1, x2, x3, x4, x5, x6) = U9_AAA(x6) 24.62/7.26 24.62/7.26 U3_AG(x1, x2, x3, x4, x5, x6) = U3_AG(x4, x6) 24.62/7.26 24.62/7.26 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x5) 24.62/7.26 24.62/7.26 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.62/7.26 24.62/7.26 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.62/7.26 24.62/7.26 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.62/7.26 24.62/7.26 U10_GA(x1, x2, x3) = U10_GA(x3) 24.62/7.26 24.62/7.26 U7_AAG(x1, x2, x3, x4, x5, x6) = U7_AAG(x1, x6) 24.62/7.26 24.62/7.26 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_AAG(x1, x2, x3, x4, x5, x6) = U9_AAG(x3, x6) 24.62/7.26 24.62/7.26 24.62/7.26 We have to consider all (P,R,Pi)-chains 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (46) 24.62/7.26 Obligation: 24.62/7.26 Pi DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> U1_AG(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 MS_IN_AG(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.62/7.26 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> U5_AAA(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.62/7.26 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AG(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U1_AG(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.26 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> SPLIT_IN_AAA(.(X, .(Y, Xs)), X1s, X2s) 24.62/7.26 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.26 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AA(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.26 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AA(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 U3_AA(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAA(Y1s, Y2s, Ys) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_AA(X, s(Y)) 24.62/7.26 LESS_IN_AA(s(X), s(Y)) -> U10_AA(X, Y, less_in_aa(X, Y)) 24.62/7.26 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.62/7.26 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_AA(Y, X) 24.62/7.26 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_AAA(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.62/7.26 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_AG(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U2_AG(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.26 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_AG(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 U3_AG(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> MERGE_IN_AAG(Y1s, Y2s, Ys) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> LESS_IN_GA(X, s(Y)) 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> U10_GA(X, Y, less_in_ga(X, Y)) 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.62/7.26 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> LESS_IN_GA(Y, X) 24.62/7.26 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_AAG(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.62/7.26 24.62/7.26 The TRS R consists of the following rules: 24.62/7.26 24.62/7.26 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.26 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.26 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.26 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.26 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.26 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.26 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.26 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.26 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.26 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.26 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.26 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.26 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.26 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.26 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.26 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.26 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.26 24.62/7.26 [] = [] 24.62/7.26 24.62/7.26 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.26 24.62/7.26 .(x1, x2) = .(x1, x2) 24.62/7.26 24.62/7.26 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.26 24.62/7.26 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.26 24.62/7.26 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.26 24.62/7.26 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.26 24.62/7.26 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.26 24.62/7.26 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.26 24.62/7.26 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.26 24.62/7.26 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.26 24.62/7.26 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.26 24.62/7.26 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.26 24.62/7.26 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.26 24.62/7.26 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.26 24.62/7.26 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.26 24.62/7.26 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.26 24.62/7.26 less_in_aa(x1, x2) = less_in_aa 24.62/7.26 24.62/7.26 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.26 24.62/7.26 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.26 24.62/7.26 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.26 24.62/7.26 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.26 24.62/7.26 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.26 24.62/7.26 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.26 24.62/7.26 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.26 24.62/7.26 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.26 24.62/7.26 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.26 24.62/7.26 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.26 24.62/7.26 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.26 24.62/7.26 0 = 0 24.62/7.26 24.62/7.26 less_out_ga(x1, x2) = less_out_ga 24.62/7.26 24.62/7.26 s(x1) = s(x1) 24.62/7.26 24.62/7.26 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.26 24.62/7.26 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.26 24.62/7.26 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.26 24.62/7.26 MS_IN_AG(x1, x2) = MS_IN_AG(x2) 24.62/7.26 24.62/7.26 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 24.62/7.26 24.62/7.26 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.62/7.26 24.62/7.26 U5_AAA(x1, x2, x3, x4, x5) = U5_AAA(x5) 24.62/7.26 24.62/7.26 U2_AG(x1, x2, x3, x4, x5, x6) = U2_AG(x4, x6) 24.62/7.26 24.62/7.26 MS_IN_AA(x1, x2) = MS_IN_AA 24.62/7.26 24.62/7.26 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.62/7.26 24.62/7.26 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.62/7.26 24.62/7.26 U3_AA(x1, x2, x3, x4, x5, x6) = U3_AA(x6) 24.62/7.26 24.62/7.26 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x5) 24.62/7.26 24.62/7.26 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.62/7.26 24.62/7.26 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.62/7.26 24.62/7.26 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.62/7.26 24.62/7.26 U10_AA(x1, x2, x3) = U10_AA(x3) 24.62/7.26 24.62/7.26 U7_AAA(x1, x2, x3, x4, x5, x6) = U7_AAA(x6) 24.62/7.26 24.62/7.26 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.62/7.26 24.62/7.26 U9_AAA(x1, x2, x3, x4, x5, x6) = U9_AAA(x6) 24.62/7.26 24.62/7.26 U3_AG(x1, x2, x3, x4, x5, x6) = U3_AG(x4, x6) 24.62/7.26 24.62/7.26 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x5) 24.62/7.26 24.62/7.26 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.62/7.26 24.62/7.26 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.62/7.26 24.62/7.26 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.62/7.26 24.62/7.26 U10_GA(x1, x2, x3) = U10_GA(x3) 24.62/7.26 24.62/7.26 U7_AAG(x1, x2, x3, x4, x5, x6) = U7_AAG(x1, x6) 24.62/7.26 24.62/7.26 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_AAG(x1, x2, x3, x4, x5, x6) = U9_AAG(x3, x6) 24.62/7.26 24.62/7.26 24.62/7.26 We have to consider all (P,R,Pi)-chains 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (47) DependencyGraphProof (EQUIVALENT) 24.62/7.26 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 23 less nodes. 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (48) 24.62/7.26 Complex Obligation (AND) 24.62/7.26 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (49) 24.62/7.26 Obligation: 24.62/7.26 Pi DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.62/7.26 24.62/7.26 The TRS R consists of the following rules: 24.62/7.26 24.62/7.26 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.26 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.26 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.26 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.26 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.26 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.26 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.26 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.26 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.26 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.26 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.26 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.26 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.26 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.26 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.26 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.26 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.26 24.62/7.26 [] = [] 24.62/7.26 24.62/7.26 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.26 24.62/7.26 .(x1, x2) = .(x1, x2) 24.62/7.26 24.62/7.26 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.26 24.62/7.26 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.26 24.62/7.26 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.26 24.62/7.26 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.26 24.62/7.26 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.26 24.62/7.26 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.26 24.62/7.26 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.26 24.62/7.26 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.26 24.62/7.26 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.26 24.62/7.26 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.26 24.62/7.26 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.26 24.62/7.26 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.26 24.62/7.26 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.26 24.62/7.26 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.26 24.62/7.26 less_in_aa(x1, x2) = less_in_aa 24.62/7.26 24.62/7.26 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.26 24.62/7.26 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.26 24.62/7.26 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.26 24.62/7.26 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.26 24.62/7.26 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.26 24.62/7.26 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.26 24.62/7.26 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.26 24.62/7.26 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.26 24.62/7.26 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.26 24.62/7.26 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.26 24.62/7.26 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.26 24.62/7.26 0 = 0 24.62/7.26 24.62/7.26 less_out_ga(x1, x2) = less_out_ga 24.62/7.26 24.62/7.26 s(x1) = s(x1) 24.62/7.26 24.62/7.26 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.26 24.62/7.26 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.26 24.62/7.26 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.26 24.62/7.26 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.26 24.62/7.26 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.62/7.26 24.62/7.26 24.62/7.26 We have to consider all (P,R,Pi)-chains 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (50) UsableRulesProof (EQUIVALENT) 24.62/7.26 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (51) 24.62/7.26 Obligation: 24.62/7.26 Pi DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 LESS_IN_GA(s(X), s(Y)) -> LESS_IN_GA(X, Y) 24.62/7.26 24.62/7.26 R is empty. 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 s(x1) = s(x1) 24.62/7.26 24.62/7.26 LESS_IN_GA(x1, x2) = LESS_IN_GA(x1) 24.62/7.26 24.62/7.26 24.62/7.26 We have to consider all (P,R,Pi)-chains 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (52) PiDPToQDPProof (SOUND) 24.62/7.26 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (53) 24.62/7.26 Obligation: 24.62/7.26 Q DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 LESS_IN_GA(s(X)) -> LESS_IN_GA(X) 24.62/7.26 24.62/7.26 R is empty. 24.62/7.26 Q is empty. 24.62/7.26 We have to consider all (P,Q,R)-chains. 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (54) QDPSizeChangeProof (EQUIVALENT) 24.62/7.26 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. 24.62/7.26 24.62/7.26 From the DPs we obtained the following set of size-change graphs: 24.62/7.26 *LESS_IN_GA(s(X)) -> LESS_IN_GA(X) 24.62/7.26 The graph contains the following edges 1 > 1 24.62/7.26 24.62/7.26 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (55) 24.62/7.26 YES 24.62/7.26 24.62/7.26 ---------------------------------------- 24.62/7.26 24.62/7.26 (56) 24.62/7.26 Obligation: 24.62/7.26 Pi DP problem: 24.62/7.26 The TRS P consists of the following rules: 24.62/7.26 24.62/7.26 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.62/7.26 24.62/7.26 The TRS R consists of the following rules: 24.62/7.26 24.62/7.26 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.26 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.26 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.26 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.26 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.26 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.26 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.26 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.26 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.26 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.26 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.26 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.26 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.26 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.26 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.26 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.26 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.26 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.26 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.26 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.26 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.26 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.26 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.26 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.26 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.26 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.26 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.26 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.26 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.26 24.62/7.26 The argument filtering Pi contains the following mapping: 24.62/7.26 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.26 24.62/7.26 [] = [] 24.62/7.26 24.62/7.26 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.26 24.62/7.26 .(x1, x2) = .(x1, x2) 24.62/7.26 24.62/7.26 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.26 24.62/7.26 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.26 24.62/7.26 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.26 24.62/7.26 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.26 24.62/7.26 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.26 24.62/7.26 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.26 24.62/7.26 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.26 24.62/7.26 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.26 24.62/7.26 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.26 24.62/7.26 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.26 24.62/7.26 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.26 24.62/7.26 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.26 24.62/7.26 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.26 24.62/7.26 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.26 24.62/7.26 less_in_aa(x1, x2) = less_in_aa 24.62/7.26 24.62/7.26 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.26 24.62/7.26 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.26 24.62/7.26 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.27 24.62/7.27 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.27 24.62/7.27 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.27 24.62/7.27 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.27 24.62/7.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.27 24.62/7.27 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.27 24.62/7.27 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.27 24.62/7.27 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.27 24.62/7.27 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.27 24.62/7.27 0 = 0 24.62/7.27 24.62/7.27 less_out_ga(x1, x2) = less_out_ga 24.62/7.27 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.27 24.62/7.27 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.27 24.62/7.27 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.27 24.62/7.27 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.27 24.62/7.27 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.62/7.27 24.62/7.27 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.62/7.27 24.62/7.27 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (57) UsableRulesProof (EQUIVALENT) 24.62/7.27 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (58) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAG(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> MERGE_IN_AAG(Xs, .(Y, Ys), Zs) 24.62/7.27 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAG(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.27 MERGE_IN_AAG(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAG(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.27 U8_AAG(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> MERGE_IN_AAG(.(X, Xs), Ys, Zs) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.27 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.27 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.27 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 .(x1, x2) = .(x1, x2) 24.62/7.27 24.62/7.27 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.27 24.62/7.27 0 = 0 24.62/7.27 24.62/7.27 less_out_ga(x1, x2) = less_out_ga 24.62/7.27 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.27 24.62/7.27 MERGE_IN_AAG(x1, x2, x3) = MERGE_IN_AAG(x3) 24.62/7.27 24.62/7.27 U6_AAG(x1, x2, x3, x4, x5, x6) = U6_AAG(x1, x5, x6) 24.62/7.27 24.62/7.27 U8_AAG(x1, x2, x3, x4, x5, x6) = U8_AAG(x3, x5, x6) 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (59) PiDPToQDPProof (SOUND) 24.62/7.27 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (60) 24.62/7.27 Obligation: 24.62/7.27 Q DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAG(X, Zs, less_out_ga) -> MERGE_IN_AAG(Zs) 24.62/7.27 MERGE_IN_AAG(.(X, Zs)) -> U6_AAG(X, Zs, less_in_ga(X)) 24.62/7.27 MERGE_IN_AAG(.(Y, Zs)) -> U8_AAG(Y, Zs, less_in_ga(Y)) 24.62/7.27 U8_AAG(Y, Zs, less_out_ga) -> MERGE_IN_AAG(Zs) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_ga(0) -> less_out_ga 24.62/7.27 less_in_ga(s(X)) -> U10_ga(less_in_ga(X)) 24.62/7.27 U10_ga(less_out_ga) -> less_out_ga 24.62/7.27 24.62/7.27 The set Q consists of the following terms: 24.62/7.27 24.62/7.27 less_in_ga(x0) 24.62/7.27 U10_ga(x0) 24.62/7.27 24.62/7.27 We have to consider all (P,Q,R)-chains. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (61) QDPSizeChangeProof (EQUIVALENT) 24.62/7.27 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. 24.62/7.27 24.62/7.27 From the DPs we obtained the following set of size-change graphs: 24.62/7.27 *MERGE_IN_AAG(.(X, Zs)) -> U6_AAG(X, Zs, less_in_ga(X)) 24.62/7.27 The graph contains the following edges 1 > 1, 1 > 2 24.62/7.27 24.62/7.27 24.62/7.27 *MERGE_IN_AAG(.(Y, Zs)) -> U8_AAG(Y, Zs, less_in_ga(Y)) 24.62/7.27 The graph contains the following edges 1 > 1, 1 > 2 24.62/7.27 24.62/7.27 24.62/7.27 *U6_AAG(X, Zs, less_out_ga) -> MERGE_IN_AAG(Zs) 24.62/7.27 The graph contains the following edges 2 >= 1 24.62/7.27 24.62/7.27 24.62/7.27 *U8_AAG(Y, Zs, less_out_ga) -> MERGE_IN_AAG(Zs) 24.62/7.27 The graph contains the following edges 2 >= 1 24.62/7.27 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (62) 24.62/7.27 YES 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (63) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.27 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.27 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.27 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.27 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.27 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.27 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.27 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.27 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.27 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.27 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.27 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.27 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.27 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.27 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.27 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.27 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.27 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.27 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.27 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.27 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.27 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.27 24.62/7.27 [] = [] 24.62/7.27 24.62/7.27 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.27 24.62/7.27 .(x1, x2) = .(x1, x2) 24.62/7.27 24.62/7.27 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.27 24.62/7.27 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.27 24.62/7.27 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.27 24.62/7.27 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.27 24.62/7.27 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.27 24.62/7.27 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.27 24.62/7.27 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.27 24.62/7.27 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.27 24.62/7.27 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.27 24.62/7.27 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.27 24.62/7.27 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.27 24.62/7.27 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.27 24.62/7.27 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.27 24.62/7.27 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.27 24.62/7.27 less_in_aa(x1, x2) = less_in_aa 24.62/7.27 24.62/7.27 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.27 24.62/7.27 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.27 24.62/7.27 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.27 24.62/7.27 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.27 24.62/7.27 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.27 24.62/7.27 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.27 24.62/7.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.27 24.62/7.27 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.27 24.62/7.27 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.27 24.62/7.27 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.27 24.62/7.27 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.27 24.62/7.27 0 = 0 24.62/7.27 24.62/7.27 less_out_ga(x1, x2) = less_out_ga 24.62/7.27 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.27 24.62/7.27 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.27 24.62/7.27 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.27 24.62/7.27 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.27 24.62/7.27 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (64) UsableRulesProof (EQUIVALENT) 24.62/7.27 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (65) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 LESS_IN_AA(s(X), s(Y)) -> LESS_IN_AA(X, Y) 24.62/7.27 24.62/7.27 R is empty. 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 LESS_IN_AA(x1, x2) = LESS_IN_AA 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (66) PiDPToQDPProof (SOUND) 24.62/7.27 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (67) 24.62/7.27 Obligation: 24.62/7.27 Q DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 LESS_IN_AA -> LESS_IN_AA 24.62/7.27 24.62/7.27 R is empty. 24.62/7.27 Q is empty. 24.62/7.27 We have to consider all (P,Q,R)-chains. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (68) NonTerminationLoopProof (COMPLETE) 24.62/7.27 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 24.62/7.27 Found a loop by semiunifying a rule from P directly. 24.62/7.27 24.62/7.27 s = LESS_IN_AA evaluates to t =LESS_IN_AA 24.62/7.27 24.62/7.27 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 24.62/7.27 * Matcher: [ ] 24.62/7.27 * Semiunifier: [ ] 24.62/7.27 24.62/7.27 -------------------------------------------------------------------------------- 24.62/7.27 Rewriting sequence 24.62/7.27 24.62/7.27 The DP semiunifies directly so there is only one rewrite step from LESS_IN_AA to LESS_IN_AA. 24.62/7.27 24.62/7.27 24.62/7.27 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (69) 24.62/7.27 NO 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (70) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.62/7.27 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.27 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.27 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.27 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.27 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.27 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.27 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.27 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.27 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.27 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.27 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.27 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.27 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.27 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.27 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.27 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.27 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.27 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.27 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.27 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.27 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.27 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.27 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.27 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.27 24.62/7.27 [] = [] 24.62/7.27 24.62/7.27 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.27 24.62/7.27 .(x1, x2) = .(x1, x2) 24.62/7.27 24.62/7.27 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.27 24.62/7.27 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.27 24.62/7.27 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.27 24.62/7.27 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.27 24.62/7.27 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.27 24.62/7.27 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.27 24.62/7.27 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.27 24.62/7.27 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.27 24.62/7.27 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.27 24.62/7.27 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.27 24.62/7.27 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.27 24.62/7.27 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.27 24.62/7.27 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.27 24.62/7.27 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.27 24.62/7.27 less_in_aa(x1, x2) = less_in_aa 24.62/7.27 24.62/7.27 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.27 24.62/7.27 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.27 24.62/7.27 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.27 24.62/7.27 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.27 24.62/7.27 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.27 24.62/7.27 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.27 24.62/7.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.27 24.62/7.27 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.27 24.62/7.27 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.27 24.62/7.27 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.27 24.62/7.27 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.27 24.62/7.27 0 = 0 24.62/7.27 24.62/7.27 less_out_ga(x1, x2) = less_out_ga 24.62/7.27 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.27 24.62/7.27 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.27 24.62/7.27 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.27 24.62/7.27 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.27 24.62/7.27 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.62/7.27 24.62/7.27 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.62/7.27 24.62/7.27 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (71) UsableRulesProof (EQUIVALENT) 24.62/7.27 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (72) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAA(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> MERGE_IN_AAA(Xs, .(Y, Ys), Zs) 24.62/7.27 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_AAA(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.27 MERGE_IN_AAA(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_AAA(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.27 U8_AAA(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> MERGE_IN_AAA(.(X, Xs), Ys, Zs) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.27 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.27 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.27 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 .(x1, x2) = .(x1, x2) 24.62/7.27 24.62/7.27 less_in_aa(x1, x2) = less_in_aa 24.62/7.27 24.62/7.27 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.27 24.62/7.27 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.27 24.62/7.27 0 = 0 24.62/7.27 24.62/7.27 s(x1) = s(x1) 24.62/7.27 24.62/7.27 MERGE_IN_AAA(x1, x2, x3) = MERGE_IN_AAA 24.62/7.27 24.62/7.27 U6_AAA(x1, x2, x3, x4, x5, x6) = U6_AAA(x6) 24.62/7.27 24.62/7.27 U8_AAA(x1, x2, x3, x4, x5, x6) = U8_AAA(x6) 24.62/7.27 24.62/7.27 24.62/7.27 We have to consider all (P,R,Pi)-chains 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (73) PiDPToQDPProof (SOUND) 24.62/7.27 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (74) 24.62/7.27 Obligation: 24.62/7.27 Q DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.62/7.27 MERGE_IN_AAA -> U6_AAA(less_in_aa) 24.62/7.27 MERGE_IN_AAA -> U8_AAA(less_in_aa) 24.62/7.27 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_aa -> less_out_aa(0) 24.62/7.27 less_in_aa -> U10_aa(less_in_aa) 24.62/7.27 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.62/7.27 24.62/7.27 The set Q consists of the following terms: 24.62/7.27 24.62/7.27 less_in_aa 24.62/7.27 U10_aa(x0) 24.62/7.27 24.62/7.27 We have to consider all (P,Q,R)-chains. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (75) TransformationProof (SOUND) 24.62/7.27 By narrowing [LPAR04] the rule MERGE_IN_AAA -> U6_AAA(less_in_aa) at position [0] we obtained the following new rules [LPAR04]: 24.62/7.27 24.62/7.27 (MERGE_IN_AAA -> U6_AAA(less_out_aa(0)),MERGE_IN_AAA -> U6_AAA(less_out_aa(0))) 24.62/7.27 (MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)),MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa))) 24.62/7.27 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (76) 24.62/7.27 Obligation: 24.62/7.27 Q DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.62/7.27 MERGE_IN_AAA -> U8_AAA(less_in_aa) 24.62/7.27 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.62/7.27 MERGE_IN_AAA -> U6_AAA(less_out_aa(0)) 24.62/7.27 MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_aa -> less_out_aa(0) 24.62/7.27 less_in_aa -> U10_aa(less_in_aa) 24.62/7.27 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.62/7.27 24.62/7.27 The set Q consists of the following terms: 24.62/7.27 24.62/7.27 less_in_aa 24.62/7.27 U10_aa(x0) 24.62/7.27 24.62/7.27 We have to consider all (P,Q,R)-chains. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (77) TransformationProof (SOUND) 24.62/7.27 By narrowing [LPAR04] the rule MERGE_IN_AAA -> U8_AAA(less_in_aa) at position [0] we obtained the following new rules [LPAR04]: 24.62/7.27 24.62/7.27 (MERGE_IN_AAA -> U8_AAA(less_out_aa(0)),MERGE_IN_AAA -> U8_AAA(less_out_aa(0))) 24.62/7.27 (MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa)),MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa))) 24.62/7.27 24.62/7.27 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (78) 24.62/7.27 Obligation: 24.62/7.27 Q DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 U6_AAA(less_out_aa(X)) -> MERGE_IN_AAA 24.62/7.27 U8_AAA(less_out_aa(Y)) -> MERGE_IN_AAA 24.62/7.27 MERGE_IN_AAA -> U6_AAA(less_out_aa(0)) 24.62/7.27 MERGE_IN_AAA -> U6_AAA(U10_aa(less_in_aa)) 24.62/7.27 MERGE_IN_AAA -> U8_AAA(less_out_aa(0)) 24.62/7.27 MERGE_IN_AAA -> U8_AAA(U10_aa(less_in_aa)) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 less_in_aa -> less_out_aa(0) 24.62/7.27 less_in_aa -> U10_aa(less_in_aa) 24.62/7.27 U10_aa(less_out_aa(X)) -> less_out_aa(s(X)) 24.62/7.27 24.62/7.27 The set Q consists of the following terms: 24.62/7.27 24.62/7.27 less_in_aa 24.62/7.27 U10_aa(x0) 24.62/7.27 24.62/7.27 We have to consider all (P,Q,R)-chains. 24.62/7.27 ---------------------------------------- 24.62/7.27 24.62/7.27 (79) 24.62/7.27 Obligation: 24.62/7.27 Pi DP problem: 24.62/7.27 The TRS P consists of the following rules: 24.62/7.27 24.62/7.27 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.62/7.27 24.62/7.27 The TRS R consists of the following rules: 24.62/7.27 24.62/7.27 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.27 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.27 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.27 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.27 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.27 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.27 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.27 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.27 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.27 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.27 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.27 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.27 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.27 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.27 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.27 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.27 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.27 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.27 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.27 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.27 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.27 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.27 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.27 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.27 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.27 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.27 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.27 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.27 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.27 24.62/7.27 The argument filtering Pi contains the following mapping: 24.62/7.27 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.27 24.62/7.27 [] = [] 24.62/7.27 24.62/7.27 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.27 24.62/7.27 .(x1, x2) = .(x1, x2) 24.62/7.27 24.62/7.27 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.27 24.62/7.27 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.27 24.62/7.27 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.27 24.62/7.27 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.27 24.62/7.27 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.27 24.62/7.27 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.27 24.62/7.27 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.27 24.62/7.27 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.27 24.62/7.27 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.27 24.62/7.27 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.27 24.62/7.27 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.27 24.62/7.27 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.27 24.62/7.27 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.27 24.62/7.27 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.27 24.62/7.27 less_in_aa(x1, x2) = less_in_aa 24.62/7.27 24.62/7.27 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.27 24.62/7.27 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.27 24.62/7.27 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.27 24.62/7.27 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.27 24.62/7.27 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.27 24.62/7.27 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.27 24.62/7.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.27 24.62/7.27 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.27 24.62/7.27 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.27 24.62/7.27 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.27 24.62/7.27 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.31 24.62/7.31 0 = 0 24.62/7.31 24.62/7.31 less_out_ga(x1, x2) = less_out_ga 24.62/7.31 24.62/7.31 s(x1) = s(x1) 24.62/7.31 24.62/7.31 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.31 24.62/7.31 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.31 24.62/7.31 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.31 24.62/7.31 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.31 24.62/7.31 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.62/7.31 24.62/7.31 24.62/7.31 We have to consider all (P,R,Pi)-chains 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (80) UsableRulesProof (EQUIVALENT) 24.62/7.31 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (81) 24.62/7.31 Obligation: 24.62/7.31 Pi DP problem: 24.62/7.31 The TRS P consists of the following rules: 24.62/7.31 24.62/7.31 SPLIT_IN_AAA(.(X, Xs), .(X, Ys), Zs) -> SPLIT_IN_AAA(Xs, Zs, Ys) 24.62/7.31 24.62/7.31 R is empty. 24.62/7.31 The argument filtering Pi contains the following mapping: 24.62/7.31 .(x1, x2) = .(x1, x2) 24.62/7.31 24.62/7.31 SPLIT_IN_AAA(x1, x2, x3) = SPLIT_IN_AAA 24.62/7.31 24.62/7.31 24.62/7.31 We have to consider all (P,R,Pi)-chains 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (82) 24.62/7.31 Obligation: 24.62/7.31 Pi DP problem: 24.62/7.31 The TRS P consists of the following rules: 24.62/7.31 24.62/7.31 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.31 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.31 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.31 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.31 24.62/7.31 The TRS R consists of the following rules: 24.62/7.31 24.62/7.31 ms_in_ag([], []) -> ms_out_ag([], []) 24.62/7.31 ms_in_ag(.(X, []), .(X, [])) -> ms_out_ag(.(X, []), .(X, [])) 24.62/7.31 ms_in_ag(.(X, .(Y, Xs)), Ys) -> U1_ag(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.31 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.31 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.31 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.31 U1_ag(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_ag(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.31 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.31 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.31 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.31 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.31 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.31 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.31 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.31 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.31 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.31 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.31 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.31 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.31 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.31 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.31 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.31 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.31 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.31 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.31 U2_ag(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_ag(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.31 U3_ag(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_ag(X, Y, Xs, Ys, merge_in_aag(Y1s, Y2s, Ys)) 24.62/7.31 merge_in_aag([], Xs, Xs) -> merge_out_aag([], Xs, Xs) 24.62/7.31 merge_in_aag(Xs, [], Xs) -> merge_out_aag(Xs, [], Xs) 24.62/7.31 merge_in_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aag(X, Xs, Y, Ys, Zs, less_in_ga(X, s(Y))) 24.62/7.31 less_in_ga(0, s(X1)) -> less_out_ga(0, s(X1)) 24.62/7.31 less_in_ga(s(X), s(Y)) -> U10_ga(X, Y, less_in_ga(X, Y)) 24.62/7.31 U10_ga(X, Y, less_out_ga(X, Y)) -> less_out_ga(s(X), s(Y)) 24.62/7.31 U6_aag(X, Xs, Y, Ys, Zs, less_out_ga(X, s(Y))) -> U7_aag(X, Xs, Y, Ys, Zs, merge_in_aag(Xs, .(Y, Ys), Zs)) 24.62/7.31 merge_in_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aag(X, Xs, Y, Ys, Zs, less_in_ga(Y, X)) 24.62/7.31 U8_aag(X, Xs, Y, Ys, Zs, less_out_ga(Y, X)) -> U9_aag(X, Xs, Y, Ys, Zs, merge_in_aag(.(X, Xs), Ys, Zs)) 24.62/7.31 U9_aag(X, Xs, Y, Ys, Zs, merge_out_aag(.(X, Xs), Ys, Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.31 U7_aag(X, Xs, Y, Ys, Zs, merge_out_aag(Xs, .(Y, Ys), Zs)) -> merge_out_aag(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.31 U4_ag(X, Y, Xs, Ys, merge_out_aag(Y1s, Y2s, Ys)) -> ms_out_ag(.(X, .(Y, Xs)), Ys) 24.62/7.31 24.62/7.31 The argument filtering Pi contains the following mapping: 24.62/7.31 ms_in_ag(x1, x2) = ms_in_ag(x2) 24.62/7.31 24.62/7.31 [] = [] 24.62/7.31 24.62/7.31 ms_out_ag(x1, x2) = ms_out_ag 24.62/7.31 24.62/7.31 .(x1, x2) = .(x1, x2) 24.62/7.31 24.62/7.31 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 24.62/7.31 24.62/7.31 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.31 24.62/7.31 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.31 24.62/7.31 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.31 24.62/7.31 U2_ag(x1, x2, x3, x4, x5, x6) = U2_ag(x4, x6) 24.62/7.31 24.62/7.31 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.31 24.62/7.31 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.31 24.62/7.31 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.31 24.62/7.31 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.31 24.62/7.31 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.31 24.62/7.31 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.31 24.62/7.31 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.31 24.62/7.31 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.31 24.62/7.31 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.31 24.62/7.31 less_in_aa(x1, x2) = less_in_aa 24.62/7.31 24.62/7.31 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.31 24.62/7.31 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.31 24.62/7.31 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.31 24.62/7.31 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.31 24.62/7.31 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.31 24.62/7.31 U3_ag(x1, x2, x3, x4, x5, x6) = U3_ag(x4, x6) 24.62/7.31 24.62/7.31 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x5) 24.62/7.31 24.62/7.31 merge_in_aag(x1, x2, x3) = merge_in_aag(x3) 24.62/7.31 24.62/7.31 merge_out_aag(x1, x2, x3) = merge_out_aag(x1, x2) 24.62/7.31 24.62/7.31 U6_aag(x1, x2, x3, x4, x5, x6) = U6_aag(x1, x5, x6) 24.62/7.31 24.62/7.31 less_in_ga(x1, x2) = less_in_ga(x1) 24.62/7.31 24.62/7.31 0 = 0 24.62/7.31 24.62/7.31 less_out_ga(x1, x2) = less_out_ga 24.62/7.31 24.62/7.31 s(x1) = s(x1) 24.62/7.31 24.62/7.31 U10_ga(x1, x2, x3) = U10_ga(x3) 24.62/7.31 24.62/7.31 U7_aag(x1, x2, x3, x4, x5, x6) = U7_aag(x1, x6) 24.62/7.31 24.62/7.31 U8_aag(x1, x2, x3, x4, x5, x6) = U8_aag(x3, x5, x6) 24.62/7.31 24.62/7.31 U9_aag(x1, x2, x3, x4, x5, x6) = U9_aag(x3, x6) 24.62/7.31 24.62/7.31 MS_IN_AA(x1, x2) = MS_IN_AA 24.62/7.31 24.62/7.31 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.62/7.31 24.62/7.31 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.62/7.31 24.62/7.31 24.62/7.31 We have to consider all (P,R,Pi)-chains 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (83) UsableRulesProof (EQUIVALENT) 24.62/7.31 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (84) 24.62/7.31 Obligation: 24.62/7.31 Pi DP problem: 24.62/7.31 The TRS P consists of the following rules: 24.62/7.31 24.62/7.31 MS_IN_AA(.(X, .(Y, Xs)), Ys) -> U1_AA(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.31 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_AA(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.31 U2_AA(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> MS_IN_AA(X2s, Y2s) 24.62/7.31 U1_AA(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> MS_IN_AA(X1s, Y1s) 24.62/7.31 24.62/7.31 The TRS R consists of the following rules: 24.62/7.31 24.62/7.31 split_in_aaa(.(X, Xs), .(X, Ys), Zs) -> U5_aaa(X, Xs, Ys, Zs, split_in_aaa(Xs, Zs, Ys)) 24.62/7.31 ms_in_aa([], []) -> ms_out_aa([], []) 24.62/7.31 ms_in_aa(.(X, []), .(X, [])) -> ms_out_aa(.(X, []), .(X, [])) 24.62/7.31 ms_in_aa(.(X, .(Y, Xs)), Ys) -> U1_aa(X, Y, Xs, Ys, split_in_aaa(.(X, .(Y, Xs)), X1s, X2s)) 24.62/7.31 U5_aaa(X, Xs, Ys, Zs, split_out_aaa(Xs, Zs, Ys)) -> split_out_aaa(.(X, Xs), .(X, Ys), Zs) 24.62/7.31 U1_aa(X, Y, Xs, Ys, split_out_aaa(.(X, .(Y, Xs)), X1s, X2s)) -> U2_aa(X, Y, Xs, Ys, X2s, ms_in_aa(X1s, Y1s)) 24.62/7.31 split_in_aaa([], [], []) -> split_out_aaa([], [], []) 24.62/7.31 U2_aa(X, Y, Xs, Ys, X2s, ms_out_aa(X1s, Y1s)) -> U3_aa(X, Y, Xs, Ys, Y1s, ms_in_aa(X2s, Y2s)) 24.62/7.31 U3_aa(X, Y, Xs, Ys, Y1s, ms_out_aa(X2s, Y2s)) -> U4_aa(X, Y, Xs, Ys, merge_in_aaa(Y1s, Y2s, Ys)) 24.62/7.31 U4_aa(X, Y, Xs, Ys, merge_out_aaa(Y1s, Y2s, Ys)) -> ms_out_aa(.(X, .(Y, Xs)), Ys) 24.62/7.31 merge_in_aaa([], Xs, Xs) -> merge_out_aaa([], Xs, Xs) 24.62/7.31 merge_in_aaa(Xs, [], Xs) -> merge_out_aaa(Xs, [], Xs) 24.62/7.31 merge_in_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) -> U6_aaa(X, Xs, Y, Ys, Zs, less_in_aa(X, s(Y))) 24.62/7.31 merge_in_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) -> U8_aaa(X, Xs, Y, Ys, Zs, less_in_aa(Y, X)) 24.62/7.31 U6_aaa(X, Xs, Y, Ys, Zs, less_out_aa(X, s(Y))) -> U7_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(Xs, .(Y, Ys), Zs)) 24.62/7.31 U8_aaa(X, Xs, Y, Ys, Zs, less_out_aa(Y, X)) -> U9_aaa(X, Xs, Y, Ys, Zs, merge_in_aaa(.(X, Xs), Ys, Zs)) 24.62/7.31 less_in_aa(0, s(X1)) -> less_out_aa(0, s(X1)) 24.62/7.31 less_in_aa(s(X), s(Y)) -> U10_aa(X, Y, less_in_aa(X, Y)) 24.62/7.31 U7_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(Xs, .(Y, Ys), Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(X, Zs)) 24.62/7.31 U9_aaa(X, Xs, Y, Ys, Zs, merge_out_aaa(.(X, Xs), Ys, Zs)) -> merge_out_aaa(.(X, Xs), .(Y, Ys), .(Y, Zs)) 24.62/7.31 U10_aa(X, Y, less_out_aa(X, Y)) -> less_out_aa(s(X), s(Y)) 24.62/7.31 24.62/7.31 The argument filtering Pi contains the following mapping: 24.62/7.31 [] = [] 24.62/7.31 24.62/7.31 .(x1, x2) = .(x1, x2) 24.62/7.31 24.62/7.31 split_in_aaa(x1, x2, x3) = split_in_aaa 24.62/7.31 24.62/7.31 split_out_aaa(x1, x2, x3) = split_out_aaa 24.62/7.31 24.62/7.31 U5_aaa(x1, x2, x3, x4, x5) = U5_aaa(x5) 24.62/7.31 24.62/7.31 ms_in_aa(x1, x2) = ms_in_aa 24.62/7.31 24.62/7.31 ms_out_aa(x1, x2) = ms_out_aa 24.62/7.31 24.62/7.31 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 24.62/7.31 24.62/7.31 U2_aa(x1, x2, x3, x4, x5, x6) = U2_aa(x6) 24.62/7.31 24.62/7.31 U3_aa(x1, x2, x3, x4, x5, x6) = U3_aa(x6) 24.62/7.31 24.62/7.31 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x5) 24.62/7.31 24.62/7.31 merge_in_aaa(x1, x2, x3) = merge_in_aaa 24.62/7.31 24.62/7.31 merge_out_aaa(x1, x2, x3) = merge_out_aaa 24.62/7.31 24.62/7.31 U6_aaa(x1, x2, x3, x4, x5, x6) = U6_aaa(x6) 24.62/7.31 24.62/7.31 less_in_aa(x1, x2) = less_in_aa 24.62/7.31 24.62/7.31 less_out_aa(x1, x2) = less_out_aa(x1) 24.62/7.31 24.62/7.31 U10_aa(x1, x2, x3) = U10_aa(x3) 24.62/7.31 24.62/7.31 U7_aaa(x1, x2, x3, x4, x5, x6) = U7_aaa(x6) 24.62/7.31 24.62/7.31 U8_aaa(x1, x2, x3, x4, x5, x6) = U8_aaa(x6) 24.62/7.31 24.62/7.31 U9_aaa(x1, x2, x3, x4, x5, x6) = U9_aaa(x6) 24.62/7.31 24.62/7.31 0 = 0 24.62/7.31 24.62/7.31 s(x1) = s(x1) 24.62/7.31 24.62/7.31 MS_IN_AA(x1, x2) = MS_IN_AA 24.62/7.31 24.62/7.31 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 24.62/7.31 24.62/7.31 U2_AA(x1, x2, x3, x4, x5, x6) = U2_AA(x6) 24.62/7.31 24.62/7.31 24.62/7.31 We have to consider all (P,R,Pi)-chains 24.62/7.31 ---------------------------------------- 24.62/7.31 24.62/7.31 (85) PrologToTRSTransformerProof (SOUND) 24.62/7.31 Transformed Prolog program to TRS. 24.62/7.31 24.62/7.31 { 24.62/7.31 "root": 29, 24.62/7.31 "program": { 24.62/7.31 "directives": [], 24.62/7.31 "clauses": [ 24.62/7.31 [ 24.62/7.31 "(ms ([]) ([]))", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(ms (. X ([])) (. X ([])))", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(ms (. X (. Y Xs)) Ys)", 24.62/7.31 "(',' (split (. X (. Y Xs)) X1s X2s) (',' (ms X1s Y1s) (',' (ms X2s Y2s) (merge Y1s Y2s Ys))))" 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(split ([]) ([]) ([]))", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(split (. X Xs) (. X Ys) Zs)", 24.62/7.31 "(split Xs Zs Ys)" 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(merge ([]) Xs Xs)", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(merge Xs ([]) Xs)", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(merge (. X Xs) (. Y Ys) (. X Zs))", 24.62/7.31 "(',' (less X (s Y)) (merge Xs (. Y Ys) Zs))" 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(merge (. X Xs) (. Y Ys) (. Y Zs))", 24.62/7.31 "(',' (less Y X) (merge (. X Xs) Ys Zs))" 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(less (0) (s X1))", 24.62/7.31 null 24.62/7.31 ], 24.62/7.31 [ 24.62/7.31 "(less (s X) (s Y))", 24.62/7.31 "(less X Y)" 24.62/7.31 ] 24.62/7.31 ] 24.62/7.31 }, 24.62/7.31 "graph": { 24.62/7.31 "nodes": { 24.62/7.31 "908": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": 5, 24.62/7.31 "scope": 9, 24.62/7.31 "term": "(merge T179 T178 T19)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": ["T19"], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "909": { 24.62/7.31 "goal": [ 24.62/7.31 { 24.62/7.31 "clause": 6, 24.62/7.31 "scope": 9, 24.62/7.31 "term": "(merge T179 T178 T19)" 24.62/7.31 }, 24.62/7.31 { 24.62/7.31 "clause": 7, 24.62/7.31 "scope": 9, 24.62/7.31 "term": "(merge T179 T178 T19)" 24.62/7.31 }, 24.62/7.31 { 24.62/7.31 "clause": 8, 24.62/7.31 "scope": 9, 24.62/7.31 "term": "(merge T179 T178 T19)" 24.62/7.31 } 24.62/7.31 ], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": ["T19"], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "type": "Nodes", 24.62/7.31 "870": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": -1, 24.62/7.31 "scope": -1, 24.62/7.31 "term": "(less T147 T148)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "750": { 24.62/7.31 "goal": [], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "871": { 24.62/7.31 "goal": [], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "234": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": 1, 24.62/7.31 "scope": 1, 24.62/7.31 "term": "(ms T1 T2)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": ["T2"], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "597": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": -1, 24.62/7.31 "scope": -1, 24.62/7.31 "term": "(split (. 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T21 T22)) X23 X24)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": [ 24.62/7.31 "X23", 24.62/7.31 "X24" 24.62/7.31 ], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "235": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": 2, 24.62/7.31 "scope": 1, 24.62/7.31 "term": "(ms T1 T2)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": ["T2"], 24.62/7.31 "free": [], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "753": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": -1, 24.62/7.31 "scope": -1, 24.62/7.31 "term": "(ms T23 X25)" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": ["X25"], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "754": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": -1, 24.62/7.31 "scope": -1, 24.62/7.31 "term": "(',' (ms T54 X26) (merge T53 X26 T19))" 24.62/7.31 }], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": ["T19"], 24.62/7.31 "free": ["X26"], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "755": { 24.62/7.31 "goal": [ 24.62/7.31 { 24.62/7.31 "clause": 0, 24.62/7.31 "scope": 5, 24.62/7.31 "term": "(ms T23 X25)" 24.62/7.31 }, 24.62/7.31 { 24.62/7.31 "clause": 1, 24.62/7.31 "scope": 5, 24.62/7.31 "term": "(ms T23 X25)" 24.62/7.31 }, 24.62/7.31 { 24.62/7.31 "clause": 2, 24.62/7.31 "scope": 5, 24.62/7.31 "term": "(ms T23 X25)" 24.62/7.31 } 24.62/7.31 ], 24.62/7.31 "kb": { 24.62/7.31 "nonunifying": [], 24.62/7.31 "intvars": {}, 24.62/7.31 "arithmetic": { 24.62/7.31 "type": "PlainIntegerRelationState", 24.62/7.31 "relations": [] 24.62/7.31 }, 24.62/7.31 "ground": [], 24.62/7.31 "free": ["X25"], 24.62/7.31 "exprvars": [] 24.62/7.31 } 24.62/7.31 }, 24.62/7.31 "877": { 24.62/7.31 "goal": [{ 24.62/7.31 "clause": -1, 24.62/7.31 "scope": -1, 24.62/7.31 "term": "(',' (less T167 T168) (merge (. 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24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "587": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "862": { 24.90/7.32 "goal": [ 24.90/7.32 { 24.90/7.32 "clause": 9, 24.90/7.32 "scope": 8, 24.90/7.32 "term": "(less T132 T133)" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "clause": 10, 24.90/7.32 "scope": 8, 24.90/7.32 "term": "(less T132 T133)" 24.90/7.32 } 24.90/7.32 ], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "983": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "863": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": 9, 24.90/7.32 "scope": 8, 24.90/7.32 "term": "(less T132 T133)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "864": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": 10, 24.90/7.32 "scope": 8, 24.90/7.32 "term": "(less T132 T133)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "744": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(true)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "986": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(less T250 T252)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": ["T250"], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "745": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "746": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "867": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(true)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "988": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "868": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "869": { 24.90/7.32 "goal": [], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "902": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(ms T54 X26)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": ["X26"], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "749": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(split T52 X80 X79)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": [], 24.90/7.32 "free": [ 24.90/7.32 "X79", 24.90/7.32 "X80" 24.90/7.32 ], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "903": { 24.90/7.32 "goal": [{ 24.90/7.32 "clause": -1, 24.90/7.32 "scope": -1, 24.90/7.32 "term": "(merge T179 T178 T19)" 24.90/7.32 }], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": ["T19"], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "905": { 24.90/7.32 "goal": [ 24.90/7.32 { 24.90/7.32 "clause": 5, 24.90/7.32 "scope": 9, 24.90/7.32 "term": "(merge T179 T178 T19)" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "clause": 6, 24.90/7.32 "scope": 9, 24.90/7.32 "term": "(merge T179 T178 T19)" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "clause": 7, 24.90/7.32 "scope": 9, 24.90/7.32 "term": "(merge T179 T178 T19)" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "clause": 8, 24.90/7.32 "scope": 9, 24.90/7.32 "term": "(merge T179 T178 T19)" 24.90/7.32 } 24.90/7.32 ], 24.90/7.32 "kb": { 24.90/7.32 "nonunifying": [], 24.90/7.32 "intvars": {}, 24.90/7.32 "arithmetic": { 24.90/7.32 "type": "PlainIntegerRelationState", 24.90/7.32 "relations": [] 24.90/7.32 }, 24.90/7.32 "ground": ["T19"], 24.90/7.32 "free": [], 24.90/7.32 "exprvars": [] 24.90/7.32 } 24.90/7.32 } 24.90/7.32 }, 24.90/7.32 "edges": [ 24.90/7.32 { 24.90/7.32 "from": 29, 24.90/7.32 "to": 30, 24.90/7.32 "label": "CASE" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 30, 24.90/7.32 "to": 31, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 30, 24.90/7.32 "to": 32, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 31, 24.90/7.32 "to": 218, 24.90/7.32 "label": "EVAL with clause\nms([], []).\nand substitutionT1 -> [],\nT2 -> []" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 31, 24.90/7.32 "to": 219, 24.90/7.32 "label": "EVAL-BACKTRACK" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 32, 24.90/7.32 "to": 234, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 32, 24.90/7.32 "to": 235, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 218, 24.90/7.32 "to": 221, 24.90/7.32 "label": "SUCCESS" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 234, 24.90/7.32 "to": 248, 24.90/7.32 "label": "EVAL with clause\nms(.(X6, []), .(X6, [])).\nand substitutionX6 -> T7,\nT1 -> .(T7, []),\nT2 -> .(T7, [])" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 234, 24.90/7.32 "to": 257, 24.90/7.32 "label": "EVAL-BACKTRACK" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 235, 24.90/7.32 "to": 585, 24.90/7.32 "label": "EVAL with clause\nms(.(X19, .(X20, X21)), X22) :- ','(split(.(X19, .(X20, X21)), X23, X24), ','(ms(X23, X25), ','(ms(X24, X26), merge(X25, X26, X22)))).\nand substitutionX19 -> T20,\nX20 -> T21,\nX21 -> T22,\nT1 -> .(T20, .(T21, T22)),\nT2 -> T19,\nX22 -> T19,\nT16 -> T20,\nT17 -> T21,\nT18 -> T22" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 235, 24.90/7.32 "to": 587, 24.90/7.32 "label": "EVAL-BACKTRACK" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 248, 24.90/7.32 "to": 262, 24.90/7.32 "label": "SUCCESS" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 585, 24.90/7.32 "to": 597, 24.90/7.32 "label": "SPLIT 1" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 585, 24.90/7.32 "to": 606, 24.90/7.32 "label": "SPLIT 2\nreplacements:X23 -> T23,\nX24 -> T24" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 597, 24.90/7.32 "to": 613, 24.90/7.32 "label": "CASE" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 606, 24.90/7.32 "to": 753, 24.90/7.32 "label": "SPLIT 1" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 606, 24.90/7.32 "to": 754, 24.90/7.32 "label": "SPLIT 2\nreplacements:X25 -> T53,\nT24 -> T54" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 613, 24.90/7.32 "to": 617, 24.90/7.32 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 617, 24.90/7.32 "to": 727, 24.90/7.32 "label": "ONLY EVAL with clause\nsplit(.(X39, X40), .(X39, X41), X42) :- split(X40, X42, X41).\nand substitutionT20 -> T33,\nX39 -> T33,\nT21 -> T36,\nT22 -> T37,\nX40 -> .(T36, T37),\nX41 -> X43,\nX23 -> .(T33, X43),\nX24 -> X44,\nX42 -> X44,\nT34 -> T36,\nT35 -> T37" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 727, 24.90/7.32 "to": 728, 24.90/7.32 "label": "CASE" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 728, 24.90/7.32 "to": 729, 24.90/7.32 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 729, 24.90/7.32 "to": 730, 24.90/7.32 "label": "ONLY EVAL with clause\nsplit(.(X57, X58), .(X57, X59), X60) :- split(X58, X60, X59).\nand substitutionT36 -> T43,\nX57 -> T43,\nT37 -> T45,\nX58 -> T45,\nX59 -> X61,\nX44 -> .(T43, X61),\nX43 -> X62,\nX60 -> X62,\nT44 -> T45" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 730, 24.90/7.32 "to": 731, 24.90/7.32 "label": "CASE" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 731, 24.90/7.32 "to": 732, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 731, 24.90/7.32 "to": 733, 24.90/7.32 "label": "PARALLEL" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 732, 24.90/7.32 "to": 744, 24.90/7.32 "label": "EVAL with clause\nsplit([], [], []).\nand substitutionT45 -> [],\nX62 -> [],\nX61 -> []" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 732, 24.90/7.32 "to": 745, 24.90/7.32 "label": "EVAL-BACKTRACK" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 733, 24.90/7.32 "to": 749, 24.90/7.32 "label": "EVAL with clause\nsplit(.(X75, X76), .(X75, X77), X78) :- split(X76, X78, X77).\nand substitutionX75 -> T50,\nX76 -> T52,\nT45 -> .(T50, T52),\nX77 -> X79,\nX62 -> .(T50, X79),\nX61 -> X80,\nX78 -> X80,\nT51 -> T52" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 733, 24.90/7.32 "to": 750, 24.90/7.32 "label": "EVAL-BACKTRACK" 24.90/7.32 }, 24.90/7.32 { 24.90/7.32 "from": 744, 24.90/7.32 "to": 746, 24.90/7.32 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 749, 24.90/7.33 "to": 730, 24.90/7.33 "label": "INSTANCE with matching:\nT45 -> T52\nX62 -> X80\nX61 -> X79" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 753, 24.90/7.33 "to": 755, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 754, 24.90/7.33 "to": 902, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 754, 24.90/7.33 "to": 903, 24.90/7.33 "label": "SPLIT 2\nreplacements:X26 -> T178,\nT53 -> T179" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 755, 24.90/7.33 "to": 757, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 755, 24.90/7.33 "to": 758, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 757, 24.90/7.33 "to": 761, 24.90/7.33 "label": "EVAL with clause\nms([], []).\nand substitutionT23 -> [],\nX25 -> []" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 757, 24.90/7.33 "to": 762, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 758, 24.90/7.33 "to": 765, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 758, 24.90/7.33 "to": 766, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 761, 24.90/7.33 "to": 763, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 765, 24.90/7.33 "to": 771, 24.90/7.33 "label": "EVAL with clause\nms(.(X85, []), .(X85, [])).\nand substitutionX85 -> T59,\nT23 -> .(T59, []),\nX25 -> .(T59, [])" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 765, 24.90/7.33 "to": 772, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 766, 24.90/7.33 "to": 777, 24.90/7.33 "label": "EVAL with clause\nms(.(X100, .(X101, X102)), X103) :- ','(split(.(X100, .(X101, X102)), X104, X105), ','(ms(X104, X106), ','(ms(X105, X107), merge(X106, X107, X103)))).\nand substitutionX100 -> T69,\nX101 -> T70,\nX102 -> T71,\nT23 -> .(T69, .(T70, T71)),\nX25 -> X108,\nX103 -> X108,\nT66 -> T69,\nT67 -> T70,\nT68 -> T71" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 766, 24.90/7.33 "to": 779, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 771, 24.90/7.33 "to": 773, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 777, 24.90/7.33 "to": 783, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 777, 24.90/7.33 "to": 784, 24.90/7.33 "label": "SPLIT 2\nreplacements:X104 -> T72,\nX105 -> T73" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 783, 24.90/7.33 "to": 597, 24.90/7.33 "label": "INSTANCE with matching:\nT20 -> T69\nT21 -> T70\nT22 -> T71\nX23 -> X104\nX24 -> X105" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 784, 24.90/7.33 "to": 792, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 784, 24.90/7.33 "to": 794, 24.90/7.33 "label": "SPLIT 2\nreplacements:X106 -> T74,\nT73 -> T75" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 792, 24.90/7.33 "to": 753, 24.90/7.33 "label": "INSTANCE with matching:\nT23 -> T72\nX25 -> X106" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 794, 24.90/7.33 "to": 801, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 794, 24.90/7.33 "to": 802, 24.90/7.33 "label": "SPLIT 2\nreplacements:X107 -> T76,\nT74 -> T77" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 801, 24.90/7.33 "to": 753, 24.90/7.33 "label": "INSTANCE with matching:\nT23 -> T75\nX25 -> X107" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 802, 24.90/7.33 "to": 807, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 807, 24.90/7.33 "to": 809, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 807, 24.90/7.33 "to": 811, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 809, 24.90/7.33 "to": 815, 24.90/7.33 "label": "EVAL with clause\nmerge([], X115, X115).\nand substitutionT77 -> [],\nT76 -> T84,\nX115 -> T84,\nX108 -> T84" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 809, 24.90/7.33 "to": 816, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 811, 24.90/7.33 "to": 818, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 811, 24.90/7.33 "to": 819, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 815, 24.90/7.33 "to": 817, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 818, 24.90/7.33 "to": 824, 24.90/7.33 "label": "EVAL with clause\nmerge(X120, [], X120).\nand substitutionT77 -> T89,\nX120 -> T89,\nT76 -> [],\nX108 -> T89" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 818, 24.90/7.33 "to": 825, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 819, 24.90/7.33 "to": 838, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 819, 24.90/7.33 "to": 839, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 824, 24.90/7.33 "to": 826, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 838, 24.90/7.33 "to": 848, 24.90/7.33 "label": "EVAL with clause\nmerge(.(X145, X146), .(X147, X148), .(X145, X149)) :- ','(less(X145, s(X147)), merge(X146, .(X147, X148), X149)).\nand substitutionX145 -> T110,\nX146 -> T112,\nT77 -> .(T110, T112),\nX147 -> T111,\nX148 -> T113,\nT76 -> .(T111, T113),\nX149 -> X150,\nX108 -> .(T110, X150),\nT106 -> T110,\nT108 -> T111,\nT107 -> T112,\nT109 -> T113" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 838, 24.90/7.33 "to": 849, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 839, 24.90/7.33 "to": 877, 24.90/7.33 "label": "EVAL with clause\nmerge(.(X195, X196), .(X197, X198), .(X197, X199)) :- ','(less(X197, X195), merge(.(X195, X196), X198, X199)).\nand substitutionX195 -> T168,\nX196 -> T170,\nT77 -> .(T168, T170),\nX197 -> T167,\nX198 -> T169,\nT76 -> .(T167, T169),\nX199 -> X200,\nX108 -> .(T167, X200),\nT165 -> T167,\nT163 -> T168,\nT166 -> T169,\nT164 -> T170" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 839, 24.90/7.33 "to": 879, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 848, 24.90/7.33 "to": 850, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 848, 24.90/7.33 "to": 851, 24.90/7.33 "label": "SPLIT 2\nnew knowledge:\nT110 is ground\nreplacements:T112 -> T116,\nT111 -> T117,\nT113 -> T118" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 850, 24.90/7.33 "to": 852, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 851, 24.90/7.33 "to": 802, 24.90/7.33 "label": "INSTANCE with matching:\nT77 -> T116\nT76 -> .(T117, T118)\nX108 -> X150" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 852, 24.90/7.33 "to": 853, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 852, 24.90/7.33 "to": 854, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 853, 24.90/7.33 "to": 855, 24.90/7.33 "label": "EVAL with clause\nless(0, s(X159)).\nand substitutionT110 -> 0,\nT111 -> T125,\nX159 -> T125" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 853, 24.90/7.33 "to": 856, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 854, 24.90/7.33 "to": 858, 24.90/7.33 "label": "EVAL with clause\nless(s(X164), s(X165)) :- less(X164, X165).\nand substitutionX164 -> T132,\nT110 -> s(T132),\nT111 -> T133,\nX165 -> T133,\nT130 -> T132,\nT131 -> T133" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 854, 24.90/7.33 "to": 859, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 855, 24.90/7.33 "to": 857, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 858, 24.90/7.33 "to": 862, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 862, 24.90/7.33 "to": 863, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 862, 24.90/7.33 "to": 864, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 863, 24.90/7.33 "to": 867, 24.90/7.33 "label": "EVAL with clause\nless(0, s(X172)).\nand substitutionT132 -> 0,\nX172 -> T140,\nT133 -> s(T140)" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 863, 24.90/7.33 "to": 868, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 864, 24.90/7.33 "to": 870, 24.90/7.33 "label": "EVAL with clause\nless(s(X177), s(X178)) :- less(X177, X178).\nand substitutionX177 -> T147,\nT132 -> s(T147),\nX178 -> T148,\nT133 -> s(T148),\nT145 -> T147,\nT146 -> T148" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 864, 24.90/7.33 "to": 871, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 867, 24.90/7.33 "to": 869, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 870, 24.90/7.33 "to": 858, 24.90/7.33 "label": "INSTANCE with matching:\nT132 -> T147\nT133 -> T148" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 877, 24.90/7.33 "to": 890, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 877, 24.90/7.33 "to": 891, 24.90/7.33 "label": "SPLIT 2\nnew knowledge:\nT167 is ground\nreplacements:T168 -> T173,\nT170 -> T174,\nT169 -> T175" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 890, 24.90/7.33 "to": 858, 24.90/7.33 "label": "INSTANCE with matching:\nT132 -> T167\nT133 -> T168" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 891, 24.90/7.33 "to": 802, 24.90/7.33 "label": "INSTANCE with matching:\nT77 -> .(T173, T174)\nT76 -> T175\nX108 -> X200" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 902, 24.90/7.33 "to": 753, 24.90/7.33 "label": "INSTANCE with matching:\nT23 -> T54\nX25 -> X26" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 903, 24.90/7.33 "to": 905, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 905, 24.90/7.33 "to": 908, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 905, 24.90/7.33 "to": 909, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 908, 24.90/7.33 "to": 910, 24.90/7.33 "label": "EVAL with clause\nmerge([], X213, X213).\nand substitutionT179 -> [],\nT178 -> T186,\nX213 -> T186,\nT19 -> T186" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 908, 24.90/7.33 "to": 911, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 909, 24.90/7.33 "to": 951, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 909, 24.90/7.33 "to": 952, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 910, 24.90/7.33 "to": 912, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 951, 24.90/7.33 "to": 954, 24.90/7.33 "label": "EVAL with clause\nmerge(X218, [], X218).\nand substitutionT179 -> T191,\nX218 -> T191,\nT178 -> [],\nT19 -> T191" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 951, 24.90/7.33 "to": 956, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 952, 24.90/7.33 "to": 960, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 952, 24.90/7.33 "to": 961, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 954, 24.90/7.33 "to": 957, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 960, 24.90/7.33 "to": 965, 24.90/7.33 "label": "EVAL with clause\nmerge(.(X239, X240), .(X241, X242), .(X239, X243)) :- ','(less(X239, s(X241)), merge(X240, .(X241, X242), X243)).\nand substitutionX239 -> T212,\nX240 -> T218,\nT179 -> .(T212, T218),\nX241 -> T217,\nX242 -> T219,\nT178 -> .(T217, T219),\nX243 -> T216,\nT19 -> .(T212, T216),\nT214 -> T217,\nT213 -> T218,\nT215 -> T219" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 960, 24.90/7.33 "to": 966, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 961, 24.90/7.33 "to": 999, 24.90/7.33 "label": "EVAL with clause\nmerge(.(X286, X287), .(X288, X289), .(X288, X290)) :- ','(less(X288, X286), merge(.(X286, X287), X289, X290)).\nand substitutionX286 -> T274,\nX287 -> T276,\nT179 -> .(T274, T276),\nX288 -> T271,\nX289 -> T275,\nT178 -> .(T271, T275),\nX290 -> T273,\nT19 -> .(T271, T273),\nT269 -> T274,\nT272 -> T275,\nT270 -> T276" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 961, 24.90/7.33 "to": 1000, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 965, 24.90/7.33 "to": 967, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 965, 24.90/7.33 "to": 968, 24.90/7.33 "label": "SPLIT 2\nnew knowledge:\nT212 is ground\nreplacements:T218 -> T222,\nT217 -> T223,\nT219 -> T224" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 967, 24.90/7.33 "to": 969, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 968, 24.90/7.33 "to": 903, 24.90/7.33 "label": "INSTANCE with matching:\nT179 -> T222\nT178 -> .(T223, T224)\nT19 -> T216" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 969, 24.90/7.33 "to": 970, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 969, 24.90/7.33 "to": 971, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 970, 24.90/7.33 "to": 972, 24.90/7.33 "label": "EVAL with clause\nless(0, s(X252)).\nand substitutionT212 -> 0,\nT217 -> T231,\nX252 -> T231" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 970, 24.90/7.33 "to": 973, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 971, 24.90/7.33 "to": 975, 24.90/7.33 "label": "EVAL with clause\nless(s(X257), s(X258)) :- less(X257, X258).\nand substitutionX257 -> T236,\nT212 -> s(T236),\nT217 -> T238,\nX258 -> T238,\nT237 -> T238" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 971, 24.90/7.33 "to": 976, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 972, 24.90/7.33 "to": 974, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 975, 24.90/7.33 "to": 978, 24.90/7.33 "label": "CASE" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 978, 24.90/7.33 "to": 979, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 978, 24.90/7.33 "to": 980, 24.90/7.33 "label": "PARALLEL" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 979, 24.90/7.33 "to": 981, 24.90/7.33 "label": "EVAL with clause\nless(0, s(X265)).\nand substitutionT236 -> 0,\nX265 -> T245,\nT238 -> s(T245)" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 979, 24.90/7.33 "to": 982, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 980, 24.90/7.33 "to": 986, 24.90/7.33 "label": "EVAL with clause\nless(s(X270), s(X271)) :- less(X270, X271).\nand substitutionX270 -> T250,\nT236 -> s(T250),\nX271 -> T252,\nT238 -> s(T252),\nT251 -> T252" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 980, 24.90/7.33 "to": 988, 24.90/7.33 "label": "EVAL-BACKTRACK" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 981, 24.90/7.33 "to": 983, 24.90/7.33 "label": "SUCCESS" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 986, 24.90/7.33 "to": 975, 24.90/7.33 "label": "INSTANCE with matching:\nT236 -> T250\nT238 -> T252" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 999, 24.90/7.33 "to": 1001, 24.90/7.33 "label": "SPLIT 1" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 999, 24.90/7.33 "to": 1002, 24.90/7.33 "label": "SPLIT 2\nnew knowledge:\nT271 is ground\nreplacements:T274 -> T279,\nT276 -> T280,\nT275 -> T281" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 1001, 24.90/7.33 "to": 975, 24.90/7.33 "label": "INSTANCE with matching:\nT236 -> T271\nT238 -> T274" 24.90/7.33 }, 24.90/7.33 { 24.90/7.33 "from": 1002, 24.90/7.33 "to": 903, 24.90/7.33 "label": "INSTANCE with matching:\nT179 -> .(T279, T280)\nT178 -> T281\nT19 -> T273" 24.90/7.33 } 24.90/7.33 ], 24.90/7.33 "type": "Graph" 24.90/7.33 } 24.90/7.33 } 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (86) 24.90/7.33 Obligation: 24.90/7.33 Q restricted rewrite system: 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (87) DependencyPairsProof (EQUIVALENT) 24.90/7.33 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (88) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F29_IN(T19) -> U1^1(f585_in(T19), T19) 24.90/7.33 F29_IN(T19) -> F585_IN(T19) 24.90/7.33 F730_IN -> U2^1(f730_in) 24.90/7.33 F730_IN -> F730_IN 24.90/7.33 F597_IN -> U3^1(f730_in) 24.90/7.33 F597_IN -> F730_IN 24.90/7.33 F753_IN -> U4^1(f777_in) 24.90/7.33 F753_IN -> F777_IN 24.90/7.33 F802_IN -> U5^1(f848_in) 24.90/7.33 F802_IN -> F848_IN 24.90/7.33 F802_IN -> U6^1(f877_in) 24.90/7.33 F802_IN -> F877_IN 24.90/7.33 F858_IN -> U7^1(f858_in) 24.90/7.33 F858_IN -> F858_IN 24.90/7.33 F903_IN(.(T212, T216)) -> U8^1(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 F903_IN(.(T212, T216)) -> F965_IN(T212, T216) 24.90/7.33 F903_IN(.(T271, T273)) -> U9^1(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 F903_IN(.(T271, T273)) -> F999_IN(T271, T273) 24.90/7.33 F975_IN(s(T250)) -> U10^1(f975_in(T250), s(T250)) 24.90/7.33 F975_IN(s(T250)) -> F975_IN(T250) 24.90/7.33 F850_IN -> U11^1(f858_in) 24.90/7.33 F850_IN -> F858_IN 24.90/7.33 F967_IN(s(T236)) -> U12^1(f975_in(T236), s(T236)) 24.90/7.33 F967_IN(s(T236)) -> F975_IN(T236) 24.90/7.33 F585_IN(T19) -> U13^1(f597_in, T19) 24.90/7.33 F585_IN(T19) -> F597_IN 24.90/7.33 U13^1(f597_out1, T19) -> U14^1(f606_in(T19), T19) 24.90/7.33 U13^1(f597_out1, T19) -> F606_IN(T19) 24.90/7.33 F606_IN(T19) -> U15^1(f753_in, T19) 24.90/7.33 F606_IN(T19) -> F753_IN 24.90/7.33 U15^1(f753_out1, T19) -> U16^1(f754_in(T19), T19) 24.90/7.33 U15^1(f753_out1, T19) -> F754_IN(T19) 24.90/7.33 F754_IN(T19) -> U17^1(f753_in, T19) 24.90/7.33 F754_IN(T19) -> F753_IN 24.90/7.33 U17^1(f753_out1, T19) -> U18^1(f903_in(T19), T19) 24.90/7.33 U17^1(f753_out1, T19) -> F903_IN(T19) 24.90/7.33 F777_IN -> U19^1(f597_in) 24.90/7.33 F777_IN -> F597_IN 24.90/7.33 U19^1(f597_out1) -> U20^1(f784_in) 24.90/7.33 U19^1(f597_out1) -> F784_IN 24.90/7.33 F784_IN -> U21^1(f753_in) 24.90/7.33 F784_IN -> F753_IN 24.90/7.33 U21^1(f753_out1) -> U22^1(f794_in) 24.90/7.33 U21^1(f753_out1) -> F794_IN 24.90/7.33 F794_IN -> U23^1(f753_in) 24.90/7.33 F794_IN -> F753_IN 24.90/7.33 U23^1(f753_out1) -> U24^1(f802_in) 24.90/7.33 U23^1(f753_out1) -> F802_IN 24.90/7.33 F848_IN -> U25^1(f850_in) 24.90/7.33 F848_IN -> F850_IN 24.90/7.33 U25^1(f850_out1(T110)) -> U26^1(f802_in, T110) 24.90/7.33 U25^1(f850_out1(T110)) -> F802_IN 24.90/7.33 F877_IN -> U27^1(f858_in) 24.90/7.33 F877_IN -> F858_IN 24.90/7.33 U27^1(f858_out1(T167)) -> U28^1(f802_in, T167) 24.90/7.33 U27^1(f858_out1(T167)) -> F802_IN 24.90/7.33 F965_IN(T212, T216) -> U29^1(f967_in(T212), T212, T216) 24.90/7.33 F965_IN(T212, T216) -> F967_IN(T212) 24.90/7.33 U29^1(f967_out1, T212, T216) -> U30^1(f903_in(T216), T212, T216) 24.90/7.33 U29^1(f967_out1, T212, T216) -> F903_IN(T216) 24.90/7.33 F999_IN(T271, T273) -> U31^1(f975_in(T271), T271, T273) 24.90/7.33 F999_IN(T271, T273) -> F975_IN(T271) 24.90/7.33 U31^1(f975_out1, T271, T273) -> U32^1(f903_in(T273), T271, T273) 24.90/7.33 U31^1(f975_out1, T271, T273) -> F903_IN(T273) 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (89) DependencyGraphProof (EQUIVALENT) 24.90/7.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 6 SCCs with 42 less nodes. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (90) 24.90/7.33 Complex Obligation (AND) 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (91) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F975_IN(s(T250)) -> F975_IN(T250) 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (92) UsableRulesProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (93) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F975_IN(s(T250)) -> F975_IN(T250) 24.90/7.33 24.90/7.33 R is empty. 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (94) QDPSizeChangeProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 24.90/7.33 From the DPs we obtained the following set of size-change graphs: 24.90/7.33 *F975_IN(s(T250)) -> F975_IN(T250) 24.90/7.33 The graph contains the following edges 1 > 1 24.90/7.33 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (95) 24.90/7.33 YES 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (96) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F903_IN(.(T212, T216)) -> F965_IN(T212, T216) 24.90/7.33 F965_IN(T212, T216) -> U29^1(f967_in(T212), T212, T216) 24.90/7.33 U29^1(f967_out1, T212, T216) -> F903_IN(T216) 24.90/7.33 F903_IN(.(T271, T273)) -> F999_IN(T271, T273) 24.90/7.33 F999_IN(T271, T273) -> U31^1(f975_in(T271), T271, T273) 24.90/7.33 U31^1(f975_out1, T271, T273) -> F903_IN(T273) 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (97) QDPSizeChangeProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 24.90/7.33 From the DPs we obtained the following set of size-change graphs: 24.90/7.33 *F965_IN(T212, T216) -> U29^1(f967_in(T212), T212, T216) 24.90/7.33 The graph contains the following edges 1 >= 2, 2 >= 3 24.90/7.33 24.90/7.33 24.90/7.33 *U29^1(f967_out1, T212, T216) -> F903_IN(T216) 24.90/7.33 The graph contains the following edges 3 >= 1 24.90/7.33 24.90/7.33 24.90/7.33 *U31^1(f975_out1, T271, T273) -> F903_IN(T273) 24.90/7.33 The graph contains the following edges 3 >= 1 24.90/7.33 24.90/7.33 24.90/7.33 *F903_IN(.(T212, T216)) -> F965_IN(T212, T216) 24.90/7.33 The graph contains the following edges 1 > 1, 1 > 2 24.90/7.33 24.90/7.33 24.90/7.33 *F903_IN(.(T271, T273)) -> F999_IN(T271, T273) 24.90/7.33 The graph contains the following edges 1 > 1, 1 > 2 24.90/7.33 24.90/7.33 24.90/7.33 *F999_IN(T271, T273) -> U31^1(f975_in(T271), T271, T273) 24.90/7.33 The graph contains the following edges 1 >= 2, 2 >= 3 24.90/7.33 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (98) 24.90/7.33 YES 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (99) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F858_IN -> F858_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (100) UsableRulesProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (101) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F858_IN -> F858_IN 24.90/7.33 24.90/7.33 R is empty. 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (102) NonTerminationLoopProof (COMPLETE) 24.90/7.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 24.90/7.33 Found a loop by semiunifying a rule from P directly. 24.90/7.33 24.90/7.33 s = F858_IN evaluates to t =F858_IN 24.90/7.33 24.90/7.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 24.90/7.33 * Matcher: [ ] 24.90/7.33 * Semiunifier: [ ] 24.90/7.33 24.90/7.33 -------------------------------------------------------------------------------- 24.90/7.33 Rewriting sequence 24.90/7.33 24.90/7.33 The DP semiunifies directly so there is only one rewrite step from F858_IN to F858_IN. 24.90/7.33 24.90/7.33 24.90/7.33 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (103) 24.90/7.33 NO 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (104) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F802_IN -> F848_IN 24.90/7.33 F848_IN -> U25^1(f850_in) 24.90/7.33 U25^1(f850_out1(T110)) -> F802_IN 24.90/7.33 F802_IN -> F877_IN 24.90/7.33 F877_IN -> U27^1(f858_in) 24.90/7.33 U27^1(f858_out1(T167)) -> F802_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (105) UsableRulesProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (106) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F802_IN -> F848_IN 24.90/7.33 F848_IN -> U25^1(f850_in) 24.90/7.33 U25^1(f850_out1(T110)) -> F802_IN 24.90/7.33 F802_IN -> F877_IN 24.90/7.33 F877_IN -> U27^1(f858_in) 24.90/7.33 U27^1(f858_out1(T167)) -> F802_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (107) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F730_IN -> F730_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (108) UsableRulesProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (109) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F730_IN -> F730_IN 24.90/7.33 24.90/7.33 R is empty. 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (110) NonTerminationLoopProof (COMPLETE) 24.90/7.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 24.90/7.33 Found a loop by semiunifying a rule from P directly. 24.90/7.33 24.90/7.33 s = F730_IN evaluates to t =F730_IN 24.90/7.33 24.90/7.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 24.90/7.33 * Matcher: [ ] 24.90/7.33 * Semiunifier: [ ] 24.90/7.33 24.90/7.33 -------------------------------------------------------------------------------- 24.90/7.33 Rewriting sequence 24.90/7.33 24.90/7.33 The DP semiunifies directly so there is only one rewrite step from F730_IN to F730_IN. 24.90/7.33 24.90/7.33 24.90/7.33 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (111) 24.90/7.33 NO 24.90/7.33 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (112) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F777_IN -> U19^1(f597_in) 24.90/7.33 U19^1(f597_out1) -> F784_IN 24.90/7.33 F784_IN -> U21^1(f753_in) 24.90/7.33 U21^1(f753_out1) -> F794_IN 24.90/7.33 F794_IN -> F753_IN 24.90/7.33 F753_IN -> F777_IN 24.90/7.33 F784_IN -> F753_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f29_in([]) -> f29_out1 24.90/7.33 f29_in(.(T7, [])) -> f29_out1 24.90/7.33 f29_in(T19) -> U1(f585_in(T19), T19) 24.90/7.33 U1(f585_out1(X25, X26), T19) -> f29_out1 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f903_in(T186) -> f903_out1([], T186) 24.90/7.33 f903_in(T191) -> f903_out1(T191, []) 24.90/7.33 f903_in(.(T212, T216)) -> U8(f965_in(T212, T216), .(T212, T216)) 24.90/7.33 U8(f965_out1(T218, T217, T219), .(T212, T216)) -> f903_out1(.(T212, T218), .(T217, T219)) 24.90/7.33 f903_in(.(T271, T273)) -> U9(f999_in(T271, T273), .(T271, T273)) 24.90/7.33 U9(f999_out1(T274, T276, T275), .(T271, T273)) -> f903_out1(.(T274, T276), .(T271, T275)) 24.90/7.33 f975_in(0) -> f975_out1 24.90/7.33 f975_in(s(T250)) -> U10(f975_in(T250), s(T250)) 24.90/7.33 U10(f975_out1, s(T250)) -> f975_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f967_in(0) -> f967_out1 24.90/7.33 f967_in(s(T236)) -> U12(f975_in(T236), s(T236)) 24.90/7.33 U12(f975_out1, s(T236)) -> f967_out1 24.90/7.33 f585_in(T19) -> U13(f597_in, T19) 24.90/7.33 U13(f597_out1, T19) -> U14(f606_in(T19), T19) 24.90/7.33 U14(f606_out1(X25, X26), T19) -> f585_out1(X25, X26) 24.90/7.33 f606_in(T19) -> U15(f753_in, T19) 24.90/7.33 U15(f753_out1, T19) -> U16(f754_in(T19), T19) 24.90/7.33 U16(f754_out1(T53, X26), T19) -> f606_out1(T53, X26) 24.90/7.33 f754_in(T19) -> U17(f753_in, T19) 24.90/7.33 U17(f753_out1, T19) -> U18(f903_in(T19), T19) 24.90/7.33 U18(f903_out1(T179, T178), T19) -> f754_out1(T179, T178) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 f965_in(T212, T216) -> U29(f967_in(T212), T212, T216) 24.90/7.33 U29(f967_out1, T212, T216) -> U30(f903_in(T216), T212, T216) 24.90/7.33 U30(f903_out1(T222, .(T223, T224)), T212, T216) -> f965_out1(T222, T223, T224) 24.90/7.33 f999_in(T271, T273) -> U31(f975_in(T271), T271, T273) 24.90/7.33 U31(f975_out1, T271, T273) -> U32(f903_in(T273), T271, T273) 24.90/7.33 U32(f903_out1(.(T279, T280), T281), T271, T273) -> f999_out1(T279, T280, T281) 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (113) UsableRulesProof (EQUIVALENT) 24.90/7.33 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. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (114) 24.90/7.33 Obligation: 24.90/7.33 Q DP problem: 24.90/7.33 The TRS P consists of the following rules: 24.90/7.33 24.90/7.33 F777_IN -> U19^1(f597_in) 24.90/7.33 U19^1(f597_out1) -> F784_IN 24.90/7.33 F784_IN -> U21^1(f753_in) 24.90/7.33 U21^1(f753_out1) -> F794_IN 24.90/7.33 F794_IN -> F753_IN 24.90/7.33 F753_IN -> F777_IN 24.90/7.33 F784_IN -> F753_IN 24.90/7.33 24.90/7.33 The TRS R consists of the following rules: 24.90/7.33 24.90/7.33 f753_in -> f753_out1 24.90/7.33 f753_in -> U4(f777_in) 24.90/7.33 f777_in -> U19(f597_in) 24.90/7.33 U4(f777_out1) -> f753_out1 24.90/7.33 f597_in -> U3(f730_in) 24.90/7.33 U19(f597_out1) -> U20(f784_in) 24.90/7.33 f784_in -> U21(f753_in) 24.90/7.33 U20(f784_out1) -> f777_out1 24.90/7.33 U21(f753_out1) -> U22(f794_in) 24.90/7.33 f794_in -> U23(f753_in) 24.90/7.33 U22(f794_out1) -> f784_out1 24.90/7.33 U23(f753_out1) -> U24(f802_in) 24.90/7.33 f802_in -> f802_out1 24.90/7.33 f802_in -> U5(f848_in) 24.90/7.33 f802_in -> U6(f877_in) 24.90/7.33 U24(f802_out1) -> f794_out1 24.90/7.33 f877_in -> U27(f858_in) 24.90/7.33 U6(f877_out1(T167)) -> f802_out1 24.90/7.33 f858_in -> f858_out1(0) 24.90/7.33 f858_in -> U7(f858_in) 24.90/7.33 U27(f858_out1(T167)) -> U28(f802_in, T167) 24.90/7.33 U28(f802_out1, T167) -> f877_out1(T167) 24.90/7.33 U7(f858_out1(T147)) -> f858_out1(s(T147)) 24.90/7.33 f848_in -> U25(f850_in) 24.90/7.33 U5(f848_out1(T110)) -> f802_out1 24.90/7.33 f850_in -> f850_out1(0) 24.90/7.33 f850_in -> U11(f858_in) 24.90/7.33 U25(f850_out1(T110)) -> U26(f802_in, T110) 24.90/7.33 U26(f802_out1, T110) -> f848_out1(T110) 24.90/7.33 U11(f858_out1(T132)) -> f850_out1(s(T132)) 24.90/7.33 f730_in -> f730_out1 24.90/7.33 f730_in -> U2(f730_in) 24.90/7.33 U3(f730_out1) -> f597_out1 24.90/7.33 U2(f730_out1) -> f730_out1 24.90/7.33 24.90/7.33 Q is empty. 24.90/7.33 We have to consider all minimal (P,Q,R)-chains. 24.90/7.33 ---------------------------------------- 24.90/7.33 24.90/7.33 (115) PrologToDTProblemTransformerProof (SOUND) 24.90/7.33 Built DT problem from termination graph DT10. 24.90/7.33 24.90/7.33 { 24.90/7.33 "root": 1, 24.90/7.33 "program": { 24.90/7.33 "directives": [], 24.90/7.33 "clauses": [ 24.90/7.33 [ 24.90/7.33 "(ms ([]) ([]))", 24.90/7.33 null 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(ms (. X ([])) (. X ([])))", 24.90/7.33 null 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(ms (. X (. Y Xs)) Ys)", 24.90/7.33 "(',' (split (. X (. Y Xs)) X1s X2s) (',' (ms X1s Y1s) (',' (ms X2s Y2s) (merge Y1s Y2s Ys))))" 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(split ([]) ([]) ([]))", 24.90/7.33 null 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(split (. X Xs) (. X Ys) Zs)", 24.90/7.33 "(split Xs Zs Ys)" 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(merge ([]) Xs Xs)", 24.90/7.33 null 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(merge Xs ([]) Xs)", 24.90/7.33 null 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(merge (. X Xs) (. Y Ys) (. X Zs))", 24.90/7.33 "(',' (less X (s Y)) (merge Xs (. Y Ys) Zs))" 24.90/7.33 ], 24.90/7.33 [ 24.90/7.33 "(merge (. X Xs) (. Y Ys) (. Y Zs))", 24.90/7.33 "(',' (less Y X) (merge (. 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T30 T29) X13)" 24.90/7.35 } 24.90/7.35 ], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": ["X13"], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "791": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": 1, 24.90/7.35 "scope": 5, 24.90/7.35 "term": "(ms (. T30 T29) X13)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": ["X13"], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "793": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": 2, 24.90/7.35 "scope": 5, 24.90/7.35 "term": "(ms (. T30 T29) X13)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": ["X13"], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "553": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": -1, 24.90/7.35 "scope": -1, 24.90/7.35 "term": "(',' (split (. T25 T26) X32 X31) (',' (ms (. 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T25 T26) X32 X31)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X31", 24.90/7.35 "X32" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "796": { 24.90/7.35 "goal": [], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "555": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": -1, 24.90/7.35 "scope": -1, 24.90/7.35 "term": "(',' (ms (. T30 T29) X13) (',' (ms T28 X14) (merge X13 X14 ([]))))" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X13", 24.90/7.35 "X14" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "797": { 24.90/7.35 "goal": [], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "556": { 24.90/7.35 "goal": [ 24.90/7.35 { 24.90/7.35 "clause": 3, 24.90/7.35 "scope": 3, 24.90/7.35 "term": "(split (. T25 T26) X32 X31)" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "clause": 4, 24.90/7.35 "scope": 3, 24.90/7.35 "term": "(split (. T25 T26) X32 X31)" 24.90/7.35 } 24.90/7.35 ], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X31", 24.90/7.35 "X32" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "557": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": 4, 24.90/7.35 "scope": 3, 24.90/7.35 "term": "(split (. T25 T26) X32 X31)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X31", 24.90/7.35 "X32" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "211": { 24.90/7.35 "goal": [ 24.90/7.35 { 24.90/7.35 "clause": 3, 24.90/7.35 "scope": 2, 24.90/7.35 "term": "(',' (split (. T10 (. T11 T12)) X11 X12) (',' (ms X11 X13) (',' (ms X12 X14) (merge X13 X14 ([])))))" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "clause": 4, 24.90/7.35 "scope": 2, 24.90/7.35 "term": "(',' (split (. T10 (. T11 T12)) X11 X12) (',' (ms X11 X13) (',' (ms X12 X14) (merge X13 X14 ([])))))" 24.90/7.35 } 24.90/7.35 ], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X11", 24.90/7.35 "X12", 24.90/7.35 "X13", 24.90/7.35 "X14" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "582": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": -1, 24.90/7.35 "scope": -1, 24.90/7.35 "term": "(split T38 X50 X49)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [ 24.90/7.35 "X49", 24.90/7.35 "X50" 24.90/7.35 ], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "900": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": -1, 24.90/7.35 "scope": -1, 24.90/7.35 "term": "(true)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "901": { 24.90/7.35 "goal": [], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "904": { 24.90/7.35 "goal": [], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": [], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "906": { 24.90/7.35 "goal": [{ 24.90/7.35 "clause": 7, 24.90/7.35 "scope": 7, 24.90/7.35 "term": "(merge T87 T86 X96)" 24.90/7.35 }], 24.90/7.35 "kb": { 24.90/7.35 "nonunifying": [], 24.90/7.35 "intvars": {}, 24.90/7.35 "arithmetic": { 24.90/7.35 "type": "PlainIntegerRelationState", 24.90/7.35 "relations": [] 24.90/7.35 }, 24.90/7.35 "ground": [], 24.90/7.35 "free": ["X96"], 24.90/7.35 "exprvars": [] 24.90/7.35 } 24.90/7.35 } 24.90/7.35 }, 24.90/7.35 "edges": [ 24.90/7.35 { 24.90/7.35 "from": 1, 24.90/7.35 "to": 5, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 5, 24.90/7.35 "to": 55, 24.90/7.35 "label": "EVAL with clause\nms([], []).\nand substitutionT1 -> [],\nT2 -> []" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 5, 24.90/7.35 "to": 56, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 55, 24.90/7.35 "to": 57, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 56, 24.90/7.35 "to": 1022, 24.90/7.35 "label": "EVAL with clause\nms(.(X246, []), .(X246, [])).\nand substitutionX246 -> T211,\nT1 -> .(T211, []),\nT2 -> .(T211, [])" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 56, 24.90/7.35 "to": 1023, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 57, 24.90/7.35 "to": 64, 24.90/7.35 "label": "BACKTRACK\nfor clause: ms(.(X, []), .(X, []))because of non-unification" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 64, 24.90/7.35 "to": 173, 24.90/7.35 "label": "EVAL with clause\nms(.(X7, .(X8, X9)), X10) :- ','(split(.(X7, .(X8, X9)), X11, X12), ','(ms(X11, X13), ','(ms(X12, X14), merge(X13, X14, X10)))).\nand substitutionX7 -> T10,\nX8 -> T11,\nX9 -> T12,\nT1 -> .(T10, .(T11, T12)),\nX10 -> [],\nT7 -> T10,\nT8 -> T11,\nT9 -> T12" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 64, 24.90/7.35 "to": 185, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 173, 24.90/7.35 "to": 211, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 211, 24.90/7.35 "to": 541, 24.90/7.35 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 541, 24.90/7.35 "to": 553, 24.90/7.35 "label": "ONLY EVAL with clause\nsplit(.(X27, X28), .(X27, X29), X30) :- split(X28, X30, X29).\nand substitutionT10 -> T27,\nX27 -> T27,\nT11 -> T25,\nT12 -> T26,\nX28 -> .(T25, T26),\nX29 -> X31,\nX11 -> .(T27, X31),\nX12 -> X32,\nX30 -> X32,\nT23 -> T25,\nT24 -> T26,\nT22 -> T27" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 553, 24.90/7.35 "to": 554, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 553, 24.90/7.35 "to": 555, 24.90/7.35 "label": "SPLIT 2\nreplacements:X32 -> T28,\nX31 -> T29,\nT27 -> T30" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 554, 24.90/7.35 "to": 556, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 555, 24.90/7.35 "to": 785, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 555, 24.90/7.35 "to": 786, 24.90/7.35 "label": "SPLIT 2\nreplacements:X13 -> T46,\nT28 -> T47" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 556, 24.90/7.35 "to": 557, 24.90/7.35 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 557, 24.90/7.35 "to": 582, 24.90/7.35 "label": "ONLY EVAL with clause\nsplit(.(X45, X46), .(X45, X47), X48) :- split(X46, X48, X47).\nand substitutionT25 -> T36,\nX45 -> T36,\nT26 -> T38,\nX46 -> T38,\nX47 -> X49,\nX32 -> .(T36, X49),\nX31 -> X50,\nX48 -> X50,\nT37 -> T38" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 582, 24.90/7.35 "to": 734, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 734, 24.90/7.35 "to": 735, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 734, 24.90/7.35 "to": 736, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 735, 24.90/7.35 "to": 737, 24.90/7.35 "label": "EVAL with clause\nsplit([], [], []).\nand substitutionT38 -> [],\nX50 -> [],\nX49 -> []" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 735, 24.90/7.35 "to": 738, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 736, 24.90/7.35 "to": 781, 24.90/7.35 "label": "EVAL with clause\nsplit(.(X63, X64), .(X63, X65), X66) :- split(X64, X66, X65).\nand substitutionX63 -> T43,\nX64 -> T45,\nT38 -> .(T43, T45),\nX65 -> X67,\nX50 -> .(T43, X67),\nX49 -> X68,\nX66 -> X68,\nT44 -> T45" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 736, 24.90/7.35 "to": 782, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 737, 24.90/7.35 "to": 739, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 781, 24.90/7.35 "to": 582, 24.90/7.35 "label": "INSTANCE with matching:\nT38 -> T45\nX50 -> X68\nX49 -> X67" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 785, 24.90/7.35 "to": 788, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 786, 24.90/7.35 "to": 1007, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 786, 24.90/7.35 "to": 1008, 24.90/7.35 "label": "SPLIT 2\nreplacements:X14 -> T188,\nT46 -> T189" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 788, 24.90/7.35 "to": 790, 24.90/7.35 "label": "BACKTRACK\nfor clause: ms([], [])because of non-unification" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 790, 24.90/7.35 "to": 791, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 790, 24.90/7.35 "to": 793, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 791, 24.90/7.35 "to": 795, 24.90/7.35 "label": "EVAL with clause\nms(.(X73, []), .(X73, [])).\nand substitutionT30 -> T52,\nX73 -> T52,\nT29 -> [],\nX13 -> .(T52, [])" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 791, 24.90/7.35 "to": 796, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 793, 24.90/7.35 "to": 805, 24.90/7.35 "label": "EVAL with clause\nms(.(X88, .(X89, X90)), X91) :- ','(split(.(X88, .(X89, X90)), X92, X93), ','(ms(X92, X94), ','(ms(X93, X95), merge(X94, X95, X91)))).\nand substitutionT30 -> T62,\nX88 -> T62,\nX89 -> T63,\nX90 -> T64,\nT29 -> .(T63, T64),\nX13 -> X96,\nX91 -> X96,\nT59 -> T62,\nT60 -> T63,\nT61 -> T64" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 793, 24.90/7.35 "to": 806, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 795, 24.90/7.35 "to": 797, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 805, 24.90/7.35 "to": 808, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 805, 24.90/7.35 "to": 810, 24.90/7.35 "label": "SPLIT 2\nreplacements:X92 -> T65,\nX93 -> T66" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 808, 24.90/7.35 "to": 554, 24.90/7.35 "label": "INSTANCE with matching:\nT25 -> T62\nT26 -> .(T63, T64)\nX32 -> X92\nX31 -> X93" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 810, 24.90/7.35 "to": 821, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 810, 24.90/7.35 "to": 822, 24.90/7.35 "label": "SPLIT 2\nreplacements:X94 -> T67,\nT66 -> T68" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 821, 24.90/7.35 "to": 827, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 822, 24.90/7.35 "to": 888, 24.90/7.35 "label": "SPLIT 1" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 822, 24.90/7.35 "to": 889, 24.90/7.35 "label": "SPLIT 2\nreplacements:X95 -> T86,\nT67 -> T87" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 827, 24.90/7.35 "to": 828, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 827, 24.90/7.35 "to": 829, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 828, 24.90/7.35 "to": 830, 24.90/7.35 "label": "EVAL with clause\nms([], []).\nand substitutionT65 -> [],\nX94 -> []" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 828, 24.90/7.35 "to": 832, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 829, 24.90/7.35 "to": 836, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 829, 24.90/7.35 "to": 837, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 830, 24.90/7.35 "to": 833, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 836, 24.90/7.35 "to": 841, 24.90/7.35 "label": "EVAL with clause\nms(.(X101, []), .(X101, [])).\nand substitutionX101 -> T73,\nT65 -> .(T73, []),\nX94 -> .(T73, [])" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 836, 24.90/7.35 "to": 843, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 837, 24.90/7.35 "to": 878, 24.90/7.35 "label": "EVAL with clause\nms(.(X116, .(X117, X118)), X119) :- ','(split(.(X116, .(X117, X118)), X120, X121), ','(ms(X120, X122), ','(ms(X121, X123), merge(X122, X123, X119)))).\nand substitutionX116 -> T83,\nX117 -> T84,\nX118 -> T85,\nT65 -> .(T83, .(T84, T85)),\nX94 -> X124,\nX119 -> X124,\nT80 -> T83,\nT81 -> T84,\nT82 -> T85" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 837, 24.90/7.35 "to": 880, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 841, 24.90/7.35 "to": 845, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 878, 24.90/7.35 "to": 805, 24.90/7.35 "label": "INSTANCE with matching:\nT62 -> T83\nT63 -> T84\nT64 -> T85\nX92 -> X120\nX93 -> X121\nX94 -> X122\nX95 -> X123\nX96 -> X124" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 888, 24.90/7.35 "to": 821, 24.90/7.35 "label": "INSTANCE with matching:\nT65 -> T68\nX94 -> X95" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 889, 24.90/7.35 "to": 892, 24.90/7.35 "label": "CASE" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 892, 24.90/7.35 "to": 893, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 892, 24.90/7.35 "to": 894, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 893, 24.90/7.35 "to": 895, 24.90/7.35 "label": "EVAL with clause\nmerge([], X131, X131).\nand substitutionT87 -> [],\nT86 -> T94,\nX131 -> T94,\nX96 -> T94" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 893, 24.90/7.35 "to": 896, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 894, 24.90/7.35 "to": 898, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 894, 24.90/7.35 "to": 899, 24.90/7.35 "label": "PARALLEL" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 895, 24.90/7.35 "to": 897, 24.90/7.35 "label": "SUCCESS" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 898, 24.90/7.35 "to": 900, 24.90/7.35 "label": "EVAL with clause\nmerge(X136, [], X136).\nand substitutionT87 -> T99,\nX136 -> T99,\nT86 -> [],\nX96 -> T99" 24.90/7.35 }, 24.90/7.35 { 24.90/7.35 "from": 898, 24.90/7.35 "to": 901, 24.90/7.35 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 899, 24.90/7.36 "to": 906, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 899, 24.90/7.36 "to": 907, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 900, 24.90/7.36 "to": 904, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 906, 24.90/7.36 "to": 953, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X161, X162), .(X163, X164), .(X161, X165)) :- ','(less(X161, s(X163)), merge(X162, .(X163, X164), X165)).\nand substitutionX161 -> T120,\nX162 -> T122,\nT87 -> .(T120, T122),\nX163 -> T121,\nX164 -> T123,\nT86 -> .(T121, T123),\nX165 -> X166,\nX96 -> .(T120, X166),\nT116 -> T120,\nT118 -> T121,\nT117 -> T122,\nT119 -> T123" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 906, 24.90/7.36 "to": 955, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 907, 24.90/7.36 "to": 1003, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X211, X212), .(X213, X214), .(X213, X215)) :- ','(less(X213, X211), merge(.(X211, X212), X214, X215)).\nand substitutionX211 -> T178,\nX212 -> T180,\nT87 -> .(T178, T180),\nX213 -> T177,\nX214 -> T179,\nT86 -> .(T177, T179),\nX215 -> X216,\nX96 -> .(T177, X216),\nT175 -> T177,\nT173 -> T178,\nT176 -> T179,\nT174 -> T180" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 907, 24.90/7.36 "to": 1004, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 953, 24.90/7.36 "to": 958, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 953, 24.90/7.36 "to": 959, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT120 is ground\nreplacements:T122 -> T126,\nT121 -> T127,\nT123 -> T128" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 958, 24.90/7.36 "to": 962, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 959, 24.90/7.36 "to": 889, 24.90/7.36 "label": "INSTANCE with matching:\nT87 -> T126\nT86 -> .(T127, T128)\nX96 -> X166" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 962, 24.90/7.36 "to": 963, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 962, 24.90/7.36 "to": 964, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 963, 24.90/7.36 "to": 984, 24.90/7.36 "label": "EVAL with clause\nless(0, s(X175)).\nand substitutionT120 -> 0,\nT121 -> T135,\nX175 -> T135" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 963, 24.90/7.36 "to": 985, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 964, 24.90/7.36 "to": 989, 24.90/7.36 "label": "EVAL with clause\nless(s(X180), s(X181)) :- less(X180, X181).\nand substitutionX180 -> T142,\nT120 -> s(T142),\nT121 -> T143,\nX181 -> T143,\nT140 -> T142,\nT141 -> T143" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 964, 24.90/7.36 "to": 990, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 984, 24.90/7.36 "to": 987, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 989, 24.90/7.36 "to": 991, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 991, 24.90/7.36 "to": 992, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 991, 24.90/7.36 "to": 993, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 992, 24.90/7.36 "to": 994, 24.90/7.36 "label": "EVAL with clause\nless(0, s(X188)).\nand substitutionT142 -> 0,\nX188 -> T150,\nT143 -> s(T150)" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 992, 24.90/7.36 "to": 995, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 993, 24.90/7.36 "to": 997, 24.90/7.36 "label": "EVAL with clause\nless(s(X193), s(X194)) :- less(X193, X194).\nand substitutionX193 -> T157,\nT142 -> s(T157),\nX194 -> T158,\nT143 -> s(T158),\nT155 -> T157,\nT156 -> T158" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 993, 24.90/7.36 "to": 998, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 994, 24.90/7.36 "to": 996, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 997, 24.90/7.36 "to": 989, 24.90/7.36 "label": "INSTANCE with matching:\nT142 -> T157\nT143 -> T158" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1003, 24.90/7.36 "to": 1005, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1003, 24.90/7.36 "to": 1006, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT177 is ground\nreplacements:T178 -> T183,\nT180 -> T184,\nT179 -> T185" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1005, 24.90/7.36 "to": 989, 24.90/7.36 "label": "INSTANCE with matching:\nT142 -> T177\nT143 -> T178" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1006, 24.90/7.36 "to": 889, 24.90/7.36 "label": "INSTANCE with matching:\nT87 -> .(T183, T184)\nT86 -> T185\nX96 -> X216" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1007, 24.90/7.36 "to": 821, 24.90/7.36 "label": "INSTANCE with matching:\nT65 -> T47\nX94 -> X14" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1008, 24.90/7.36 "to": 1009, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1009, 24.90/7.36 "to": 1010, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1009, 24.90/7.36 "to": 1011, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1010, 24.90/7.36 "to": 1012, 24.90/7.36 "label": "EVAL with clause\nmerge([], X229, X229).\nand substitutionT189 -> [],\nT188 -> [],\nX229 -> [],\nT196 -> []" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1010, 24.90/7.36 "to": 1013, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1011, 24.90/7.36 "to": 1015, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1011, 24.90/7.36 "to": 1016, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1012, 24.90/7.36 "to": 1014, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1015, 24.90/7.36 "to": 1017, 24.90/7.36 "label": "EVAL with clause\nmerge(X234, [], X234).\nand substitutionT189 -> [],\nX234 -> [],\nT188 -> [],\nT201 -> []" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1015, 24.90/7.36 "to": 1018, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1016, 24.90/7.36 "to": 1020, 24.90/7.36 "label": "BACKTRACK\nfor clause: merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(less(X, s(Y)), merge(Xs, .(Y, Ys), Zs))because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1017, 24.90/7.36 "to": 1019, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1020, 24.90/7.36 "to": 1021, 24.90/7.36 "label": "BACKTRACK\nfor clause: merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(less(Y, X), merge(.(X, Xs), Ys, Zs))because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1022, 24.90/7.36 "to": 1024, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1023, 24.90/7.36 "to": 1121, 24.90/7.36 "label": "EVAL with clause\nms(.(X345, .(X346, X347)), X348) :- ','(split(.(X345, .(X346, X347)), X349, X350), ','(ms(X349, X351), ','(ms(X350, X352), merge(X351, X352, X348)))).\nand substitutionX345 -> T333,\nX346 -> T334,\nX347 -> T335,\nT1 -> .(T333, .(T334, T335)),\nT2 -> T332,\nX348 -> T332,\nT329 -> T333,\nT330 -> T334,\nT331 -> T335" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1023, 24.90/7.36 "to": 1122, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1024, 24.90/7.36 "to": 1025, 24.90/7.36 "label": "EVAL with clause\nms(.(X251, .(X252, X253)), X254) :- ','(split(.(X251, .(X252, X253)), X255, X256), ','(ms(X255, X257), ','(ms(X256, X258), merge(X257, X258, X254)))).\nand substitutionX251 -> T220,\nX252 -> T221,\nX253 -> T222,\nT1 -> .(T220, .(T221, T222)),\nT211 -> T219,\nX254 -> .(T219, []),\nT216 -> T220,\nT217 -> T221,\nT218 -> T222" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1024, 24.90/7.36 "to": 1026, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1025, 24.90/7.36 "to": 1027, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1027, 24.90/7.36 "to": 1028, 24.90/7.36 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1028, 24.90/7.36 "to": 1067, 24.90/7.36 "label": "ONLY EVAL with clause\nsplit(.(X271, X272), .(X271, X273), X274) :- split(X272, X274, X273).\nand substitutionT220 -> T237,\nX271 -> T237,\nT221 -> T235,\nT222 -> T236,\nX272 -> .(T235, T236),\nX273 -> X275,\nX255 -> .(T237, X275),\nX256 -> X276,\nX274 -> X276,\nT233 -> T235,\nT234 -> T236,\nT232 -> T237" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1067, 24.90/7.36 "to": 1068, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1067, 24.90/7.36 "to": 1069, 24.90/7.36 "label": "SPLIT 2\nreplacements:X276 -> T238,\nX275 -> T239,\nT237 -> T240" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1068, 24.90/7.36 "to": 554, 24.90/7.36 "label": "INSTANCE with matching:\nT25 -> T235\nT26 -> T236\nX32 -> X276\nX31 -> X275" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1069, 24.90/7.36 "to": 1070, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1069, 24.90/7.36 "to": 1071, 24.90/7.36 "label": "SPLIT 2\nreplacements:X257 -> T241,\nT238 -> T242" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1070, 24.90/7.36 "to": 785, 24.90/7.36 "label": "INSTANCE with matching:\nT30 -> T240\nT29 -> T239\nX13 -> X257" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1071, 24.90/7.36 "to": 1096, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1071, 24.90/7.36 "to": 1097, 24.90/7.36 "label": "SPLIT 2\nreplacements:X258 -> T243,\nT241 -> T244" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1096, 24.90/7.36 "to": 821, 24.90/7.36 "label": "INSTANCE with matching:\nT65 -> T242\nX94 -> X258" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1097, 24.90/7.36 "to": 1098, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1098, 24.90/7.36 "to": 1099, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1098, 24.90/7.36 "to": 1100, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1099, 24.90/7.36 "to": 1101, 24.90/7.36 "label": "EVAL with clause\nmerge([], X283, X283).\nand substitutionT244 -> [],\nT243 -> .(T258, []),\nX283 -> .(T258, []),\nT219 -> T258,\nT257 -> .(T258, [])" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1099, 24.90/7.36 "to": 1102, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1100, 24.90/7.36 "to": 1104, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1100, 24.90/7.36 "to": 1105, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1101, 24.90/7.36 "to": 1103, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1104, 24.90/7.36 "to": 1106, 24.90/7.36 "label": "EVAL with clause\nmerge(X288, [], X288).\nand substitutionT244 -> .(T268, []),\nX288 -> .(T268, []),\nT243 -> [],\nT219 -> T268,\nT267 -> .(T268, [])" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1104, 24.90/7.36 "to": 1107, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1105, 24.90/7.36 "to": 1109, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1105, 24.90/7.36 "to": 1110, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1106, 24.90/7.36 "to": 1108, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1109, 24.90/7.36 "to": 1111, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X309, X310), .(X311, X312), .(X309, X313)) :- ','(less(X309, s(X311)), merge(X310, .(X311, X312), X313)).\nand substitutionX309 -> T285,\nX310 -> T290,\nT244 -> .(T285, T290),\nX311 -> T289,\nX312 -> T291,\nT243 -> .(T289, T291),\nT219 -> T285,\nX313 -> [],\nT287 -> T289,\nT286 -> T290,\nT288 -> T291" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1109, 24.90/7.36 "to": 1112, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1110, 24.90/7.36 "to": 1117, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X330, X331), .(X332, X333), .(X332, X334)) :- ','(less(X332, X330), merge(.(X330, X331), X333, X334)).\nand substitutionX330 -> T315,\nX331 -> T317,\nT244 -> .(T315, T317),\nX332 -> T313,\nX333 -> T316,\nT243 -> .(T313, T316),\nT219 -> T313,\nX334 -> [],\nT311 -> T315,\nT314 -> T316,\nT312 -> T317" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1110, 24.90/7.36 "to": 1118, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1111, 24.90/7.36 "to": 1113, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1111, 24.90/7.36 "to": 1114, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT285 is ground\nreplacements:T290 -> T294,\nT289 -> T295,\nT291 -> T296" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1113, 24.90/7.36 "to": 958, 24.90/7.36 "label": "INSTANCE with matching:\nT120 -> T285\nT121 -> T289" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1114, 24.90/7.36 "to": 1008, 24.90/7.36 "label": "INSTANCE with matching:\nT189 -> T294\nT188 -> .(T295, T296)" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1117, 24.90/7.36 "to": 1119, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1117, 24.90/7.36 "to": 1120, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT313 is ground\nreplacements:T315 -> T320,\nT317 -> T321,\nT316 -> T322" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1119, 24.90/7.36 "to": 989, 24.90/7.36 "label": "INSTANCE with matching:\nT142 -> T313\nT143 -> T315" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1120, 24.90/7.36 "to": 1008, 24.90/7.36 "label": "INSTANCE with matching:\nT189 -> .(T320, T321)\nT188 -> T322" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1121, 24.90/7.36 "to": 1123, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1123, 24.90/7.36 "to": 1124, 24.90/7.36 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1124, 24.90/7.36 "to": 1125, 24.90/7.36 "label": "ONLY EVAL with clause\nsplit(.(X365, X366), .(X365, X367), X368) :- split(X366, X368, X367).\nand substitutionT333 -> T350,\nX365 -> T350,\nT334 -> T348,\nT335 -> T349,\nX366 -> .(T348, T349),\nX367 -> X369,\nX349 -> .(T350, X369),\nX350 -> X370,\nX368 -> X370,\nT346 -> T348,\nT347 -> T349,\nT345 -> T350" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1125, 24.90/7.36 "to": 1126, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1125, 24.90/7.36 "to": 1127, 24.90/7.36 "label": "SPLIT 2\nreplacements:X370 -> T351,\nX369 -> T352,\nT350 -> T353,\nT1 -> T354" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1126, 24.90/7.36 "to": 554, 24.90/7.36 "label": "INSTANCE with matching:\nT25 -> T348\nT26 -> T349\nX32 -> X370\nX31 -> X369" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1127, 24.90/7.36 "to": 1128, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1127, 24.90/7.36 "to": 1129, 24.90/7.36 "label": "SPLIT 2\nreplacements:X351 -> T355,\nT351 -> T356,\nT354 -> T357" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1128, 24.90/7.36 "to": 785, 24.90/7.36 "label": "INSTANCE with matching:\nT30 -> T353\nT29 -> T352\nX13 -> X351" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1129, 24.90/7.36 "to": 1130, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1129, 24.90/7.36 "to": 1131, 24.90/7.36 "label": "SPLIT 2\nreplacements:X352 -> T358,\nT355 -> T359,\nT357 -> T360" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1130, 24.90/7.36 "to": 821, 24.90/7.36 "label": "INSTANCE with matching:\nT65 -> T356\nX94 -> X352" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1131, 24.90/7.36 "to": 1132, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1132, 24.90/7.36 "to": 1133, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1132, 24.90/7.36 "to": 1134, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1133, 24.90/7.36 "to": 1135, 24.90/7.36 "label": "EVAL with clause\nmerge([], X377, X377).\nand substitutionT359 -> [],\nT358 -> T367,\nX377 -> T367,\nT332 -> T367" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1133, 24.90/7.36 "to": 1136, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1134, 24.90/7.36 "to": 1138, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1134, 24.90/7.36 "to": 1139, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1135, 24.90/7.36 "to": 1137, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1138, 24.90/7.36 "to": 1140, 24.90/7.36 "label": "EVAL with clause\nmerge(X382, [], X382).\nand substitutionT359 -> T372,\nX382 -> T372,\nT358 -> [],\nT332 -> T372" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1138, 24.90/7.36 "to": 1141, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1139, 24.90/7.36 "to": 1143, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1139, 24.90/7.36 "to": 1144, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1140, 24.90/7.36 "to": 1142, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1143, 24.90/7.36 "to": 1145, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X403, X404), .(X405, X406), .(X403, X407)) :- ','(less(X403, s(X405)), merge(X404, .(X405, X406), X407)).\nand substitutionX403 -> T393,\nX404 -> T399,\nT359 -> .(T393, T399),\nX405 -> T398,\nX406 -> T400,\nT358 -> .(T398, T400),\nX407 -> T397,\nT332 -> .(T393, T397),\nT395 -> T398,\nT394 -> T399,\nT396 -> T400" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1143, 24.90/7.36 "to": 1146, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1144, 24.90/7.36 "to": 1192, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X582, X583), .(X584, X585), .(X584, X586)) :- ','(less(X584, X582), merge(.(X582, X583), X585, X586)).\nand substitutionX582 -> T624,\nX583 -> T626,\nT359 -> .(T624, T626),\nX584 -> T621,\nX585 -> T625,\nT358 -> .(T621, T625),\nX586 -> T623,\nT332 -> .(T621, T623),\nT619 -> T624,\nT622 -> T625,\nT620 -> T626" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1144, 24.90/7.36 "to": 1193, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1145, 24.90/7.36 "to": 1147, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1145, 24.90/7.36 "to": 1148, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT393 is ground\nreplacements:T399 -> T403,\nT398 -> T404,\nT400 -> T405,\nT360 -> T406" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1147, 24.90/7.36 "to": 958, 24.90/7.36 "label": "INSTANCE with matching:\nT120 -> T393\nT121 -> T398" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1148, 24.90/7.36 "to": 1149, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1149, 24.90/7.36 "to": 1150, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1149, 24.90/7.36 "to": 1151, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1150, 24.90/7.36 "to": 1152, 24.90/7.36 "label": "EVAL with clause\nmerge([], X418, X418).\nand substitutionT403 -> [],\nT404 -> T421,\nT405 -> T422,\nX418 -> .(T421, T422),\nT397 -> .(T421, T422)" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1150, 24.90/7.36 "to": 1153, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1151, 24.90/7.36 "to": 1155, 24.90/7.36 "label": "BACKTRACK\nfor clause: merge(Xs, [], Xs)because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1152, 24.90/7.36 "to": 1154, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1155, 24.90/7.36 "to": 1156, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1155, 24.90/7.36 "to": 1157, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1156, 24.90/7.36 "to": 1158, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X440, X441), .(X442, X443), .(X440, X444)) :- ','(less(X440, s(X442)), merge(X441, .(X442, X443), X444)).\nand substitutionX440 -> T444,\nX441 -> T450,\nT403 -> .(T444, T450),\nT404 -> T449,\nX442 -> T449,\nT405 -> T451,\nX443 -> T451,\nX444 -> T448,\nT397 -> .(T444, T448),\nT446 -> T449,\nT445 -> T450,\nT447 -> T451" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1156, 24.90/7.36 "to": 1159, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1157, 24.90/7.36 "to": 1190, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X565, X566), .(X567, X568), .(X567, X569)) :- ','(less(X567, X565), merge(.(X565, X566), X568, X569)).\nand substitutionX565 -> T604,\nX566 -> T606,\nT403 -> .(T604, T606),\nT404 -> T601,\nX567 -> T601,\nT405 -> T605,\nX568 -> T605,\nX569 -> T603,\nT397 -> .(T601, T603),\nT599 -> T604,\nT602 -> T605,\nT600 -> T606" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1157, 24.90/7.36 "to": 1191, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1158, 24.90/7.36 "to": 1160, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1158, 24.90/7.36 "to": 1161, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT444 is ground\nreplacements:T450 -> T454,\nT449 -> T455,\nT451 -> T456" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1160, 24.90/7.36 "to": 958, 24.90/7.36 "label": "INSTANCE with matching:\nT120 -> T444\nT121 -> T449" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1161, 24.90/7.36 "to": 1162, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1162, 24.90/7.36 "to": 1163, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1162, 24.90/7.36 "to": 1164, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1163, 24.90/7.36 "to": 1165, 24.90/7.36 "label": "EVAL with clause\nmerge([], X455, X455).\nand substitutionT454 -> [],\nT455 -> T471,\nT456 -> T472,\nX455 -> .(T471, T472),\nT448 -> .(T471, T472)" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1163, 24.90/7.36 "to": 1166, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1164, 24.90/7.36 "to": 1168, 24.90/7.36 "label": "BACKTRACK\nfor clause: merge(Xs, [], Xs)because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1165, 24.90/7.36 "to": 1167, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1168, 24.90/7.36 "to": 1169, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1168, 24.90/7.36 "to": 1170, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1169, 24.90/7.36 "to": 1171, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X477, X478), .(X479, X480), .(X477, X481)) :- ','(less(X477, s(X479)), merge(X478, .(X479, X480), X481)).\nand substitutionX477 -> T494,\nX478 -> T500,\nT454 -> .(T494, T500),\nT455 -> T499,\nX479 -> T499,\nT456 -> T501,\nX480 -> T501,\nX481 -> T498,\nT448 -> .(T494, T498),\nT496 -> T499,\nT495 -> T500,\nT497 -> T501" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1169, 24.90/7.36 "to": 1172, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1170, 24.90/7.36 "to": 1173, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X494, X495), .(X496, X497), .(X496, X498)) :- ','(less(X496, X494), merge(.(X494, X495), X497, X498)).\nand substitutionX494 -> T519,\nX495 -> T521,\nT454 -> .(T519, T521),\nT455 -> T516,\nX496 -> T516,\nT456 -> T520,\nX497 -> T520,\nX498 -> T518,\nT448 -> .(T516, T518),\nT514 -> T519,\nT517 -> T520,\nT515 -> T521" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1170, 24.90/7.36 "to": 1174, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1171, 24.90/7.36 "to": 1158, 24.90/7.36 "label": "INSTANCE with matching:\nT444 -> T494\nT449 -> T499\nT450 -> T500\nT451 -> T501\nT448 -> T498" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1173, 24.90/7.36 "to": 1175, 24.90/7.36 "label": "SPLIT 1" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1173, 24.90/7.36 "to": 1176, 24.90/7.36 "label": "SPLIT 2\nnew knowledge:\nT516 is ground\nreplacements:T519 -> T524,\nT521 -> T525,\nT520 -> T526" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1175, 24.90/7.36 "to": 989, 24.90/7.36 "label": "INSTANCE with matching:\nT142 -> T516\nT143 -> T519" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1176, 24.90/7.36 "to": 1177, 24.90/7.36 "label": "CASE" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1177, 24.90/7.36 "to": 1178, 24.90/7.36 "label": "BACKTRACK\nfor clause: merge([], Xs, Xs)because of non-unification" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1178, 24.90/7.36 "to": 1179, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1178, 24.90/7.36 "to": 1180, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1179, 24.90/7.36 "to": 1181, 24.90/7.36 "label": "EVAL with clause\nmerge(X510, [], X510).\nand substitutionT524 -> T537,\nT525 -> T538,\nX510 -> .(T537, T538),\nT526 -> [],\nT518 -> .(T537, T538)" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1179, 24.90/7.36 "to": 1182, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1180, 24.90/7.36 "to": 1184, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1180, 24.90/7.36 "to": 1185, 24.90/7.36 "label": "PARALLEL" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1181, 24.90/7.36 "to": 1183, 24.90/7.36 "label": "SUCCESS" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1184, 24.90/7.36 "to": 1186, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X531, X532), .(X533, X534), .(X531, X535)) :- ','(less(X531, s(X533)), merge(X532, .(X533, X534), X535)).\nand substitutionT524 -> T559,\nX531 -> T559,\nT525 -> T565,\nX532 -> T565,\nX533 -> T564,\nX534 -> T566,\nT526 -> .(T564, T566),\nX535 -> T563,\nT518 -> .(T559, T563),\nT561 -> T564,\nT560 -> T565,\nT562 -> T566" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1184, 24.90/7.36 "to": 1187, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1185, 24.90/7.36 "to": 1188, 24.90/7.36 "label": "EVAL with clause\nmerge(.(X548, X549), .(X550, X551), .(X550, X552)) :- ','(less(X550, X548), merge(.(X548, X549), X551, X552)).\nand substitutionT524 -> T584,\nX548 -> T584,\nT525 -> T586,\nX549 -> T586,\nX550 -> T581,\nX551 -> T585,\nT526 -> .(T581, T585),\nX552 -> T583,\nT518 -> .(T581, T583),\nT579 -> T584,\nT582 -> T585,\nT580 -> T586" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1185, 24.90/7.36 "to": 1189, 24.90/7.36 "label": "EVAL-BACKTRACK" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1186, 24.90/7.36 "to": 1158, 24.90/7.36 "label": "INSTANCE with matching:\nT444 -> T559\nT449 -> T564\nT450 -> T565\nT451 -> T566\nT448 -> T563" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1188, 24.90/7.36 "to": 1173, 24.90/7.36 "label": "INSTANCE with matching:\nT516 -> T581\nT519 -> T584\nT521 -> T586\nT520 -> T585\nT518 -> T583" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1190, 24.90/7.36 "to": 1173, 24.90/7.36 "label": "INSTANCE with matching:\nT516 -> T601\nT519 -> T604\nT521 -> T606\nT520 -> T605\nT518 -> T603" 24.90/7.36 }, 24.90/7.36 { 24.90/7.36 "from": 1192, 24.90/7.36 "to": 1173, 24.90/7.36 "label": "INSTANCE with matching:\nT516 -> T621\nT519 -> T624\nT521 -> T626\nT520 -> T625\nT518 -> T623" 24.90/7.36 } 24.90/7.36 ], 24.90/7.36 "type": "Graph" 24.90/7.36 } 24.90/7.36 } 24.90/7.36 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (116) 24.90/7.36 Obligation: 24.90/7.36 Triples: 24.90/7.36 24.90/7.36 splitA(.(X1, X2), .(X1, X3), X4) :- splitA(X2, X4, X3). 24.90/7.36 splitB(X1, X2, .(X1, X3), X4) :- splitA(X2, X4, X3). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- splitB(X1, .(X2, X3), X4, X5). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), msE(X4, X6)). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), msE(X5, X7))). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), ','(mscE(X5, X7), mergeD(X6, X7, X8)))). 24.90/7.36 msE(.(X1, .(X2, X3)), X4) :- pC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X1, X5)) :- lessF(X1, X3). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X1, X5)) :- ','(lesscF(X1, X3), mergeD(X2, .(X3, X4), X5)). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X3, X5)) :- lessG(X3, X1). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X3, X5)) :- ','(lesscG(X3, X1), mergeD(.(X1, X2), X4, X5)). 24.90/7.36 lessG(s(X1), s(X2)) :- lessG(X1, X2). 24.90/7.36 msH(X1, .(X2, X3), X4) :- pC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 lessF(s(X1), X2) :- lessG(X1, X2). 24.90/7.36 pJ(X1, X2, X3, X4, X5) :- lessF(X1, X2). 24.90/7.36 pJ(X1, X2, .(X3, X4), X5, .(X3, X6)) :- ','(lesscF(X1, X2), pJ(X3, X2, X4, X5, X6)). 24.90/7.36 pJ(X1, X2, .(X3, X4), X5, .(X2, X6)) :- ','(lesscF(X1, X2), pK(X2, X3, X4, X5, X6)). 24.90/7.36 pK(X1, X2, X3, X4, X5) :- lessG(X1, X2). 24.90/7.36 pK(X1, X2, X3, .(X4, X5), .(X2, X6)) :- ','(lesscG(X1, X2), pJ(X2, X4, X3, X5, X6)). 24.90/7.36 pK(X1, X2, X3, .(X4, X5), .(X4, X6)) :- ','(lesscG(X1, X2), pK(X4, X2, X3, X5, X6)). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- splitB(X2, X3, X4, X5). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- ','(splitcB(X2, X3, X4, X5), msH(X1, X5, X6)). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- ','(splitcB(X2, X3, X4, X5), ','(mscH(X1, X5, X6), msE(X4, X7))). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- ','(splitcB(X2, X3, X4, X5), ','(mscH(X1, X5, X6), ','(mscE(X4, X7), mergeI(X6, X7)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- splitB(X2, X3, X5, X6). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), msH(X1, X6, X7)). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, X7), msE(X5, X8))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X4, X7)), ','(mscE(X5, .(X8, X9)), lessF(X4, X8)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X4, X7)), ','(mscE(X5, .(X8, X9)), ','(lesscF(X4, X8), mergeI(X7, .(X8, X9)))))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X7, X8)), ','(mscE(X5, .(X4, X9)), lessG(X4, X7)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X7, X8)), ','(mscE(X5, .(X4, X9)), ','(lesscG(X4, X7), mergeI(.(X7, X8), X9))))). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- splitB(X2, X3, X5, X6). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- ','(splitcB(X2, X3, X5, X6), msH(X1, X6, X7)). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, X7), msE(X5, X8))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, X5)) :- ','(splitcB(X2, X3, X6, X7), ','(mscH(X1, X7, .(X4, X8)), ','(mscE(X6, .(X9, X10)), lessF(X4, X9)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, .(X5, X6))) :- ','(splitcB(X2, X3, X7, X8), ','(mscH(X1, X8, .(X4, .(X5, X9))), ','(mscE(X7, .(X10, X11)), ','(lesscF(X4, X10), pJ(X5, X10, X9, X11, X6))))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, .(X5, X6))) :- ','(splitcB(X2, X3, X7, X8), ','(mscH(X1, X8, .(X4, .(X9, X10))), ','(mscE(X7, .(X5, X11)), ','(lesscF(X4, X5), pK(X5, X9, X10, X11, X6))))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, X5)) :- ','(splitcB(X2, X3, X6, X7), ','(mscH(X1, X7, .(X8, X9)), ','(mscE(X6, .(X4, X10)), pK(X4, X8, X9, X10, X5)))). 24.90/7.36 24.90/7.36 Clauses: 24.90/7.36 24.90/7.36 splitcA([], [], []). 24.90/7.36 splitcA(.(X1, X2), .(X1, X3), X4) :- splitcA(X2, X4, X3). 24.90/7.36 splitcB(X1, X2, .(X1, X3), X4) :- splitcA(X2, X4, X3). 24.90/7.36 qcC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), ','(mscE(X5, X7), mergecD(X6, X7, X8)))). 24.90/7.36 mscE([], []). 24.90/7.36 mscE(.(X1, []), .(X1, [])). 24.90/7.36 mscE(.(X1, .(X2, X3)), X4) :- qcC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 mergecD([], X1, X1). 24.90/7.36 mergecD(X1, [], X1). 24.90/7.36 mergecD(.(X1, X2), .(X3, X4), .(X1, X5)) :- ','(lesscF(X1, X3), mergecD(X2, .(X3, X4), X5)). 24.90/7.36 mergecD(.(X1, X2), .(X3, X4), .(X3, X5)) :- ','(lesscG(X3, X1), mergecD(.(X1, X2), X4, X5)). 24.90/7.36 lesscG(0, s(X1)). 24.90/7.36 lesscG(s(X1), s(X2)) :- lesscG(X1, X2). 24.90/7.36 mscH(X1, [], .(X1, [])). 24.90/7.36 mscH(X1, .(X2, X3), X4) :- qcC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 lesscF(0, X1). 24.90/7.36 lesscF(s(X1), X2) :- lesscG(X1, X2). 24.90/7.36 mergecI([], []). 24.90/7.36 mergecI([], []). 24.90/7.36 qcJ(X1, X2, [], X3, .(X2, X3)) :- lesscF(X1, X2). 24.90/7.36 qcJ(X1, X2, .(X3, X4), X5, .(X3, X6)) :- ','(lesscF(X1, X2), qcJ(X3, X2, X4, X5, X6)). 24.90/7.36 qcJ(X1, X2, .(X3, X4), X5, .(X2, X6)) :- ','(lesscF(X1, X2), qcK(X2, X3, X4, X5, X6)). 24.90/7.36 qcK(X1, X2, X3, [], .(X2, X3)) :- lesscG(X1, X2). 24.90/7.36 qcK(X1, X2, X3, .(X4, X5), .(X2, X6)) :- ','(lesscG(X1, X2), qcJ(X2, X4, X3, X5, X6)). 24.90/7.36 qcK(X1, X2, X3, .(X4, X5), .(X4, X6)) :- ','(lesscG(X1, X2), qcK(X4, X2, X3, X5, X6)). 24.90/7.36 24.90/7.36 Afs: 24.90/7.36 24.90/7.36 msL(x1, x2) = msL(x2) 24.90/7.36 24.90/7.36 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (117) UndefinedPredicateInTriplesTransformerProof (SOUND) 24.90/7.36 Deleted triples and predicates having undefined goals [DT09]. 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (118) 24.90/7.36 Obligation: 24.90/7.36 Triples: 24.90/7.36 24.90/7.36 splitA(.(X1, X2), .(X1, X3), X4) :- splitA(X2, X4, X3). 24.90/7.36 splitB(X1, X2, .(X1, X3), X4) :- splitA(X2, X4, X3). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- splitB(X1, .(X2, X3), X4, X5). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), msE(X4, X6)). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), msE(X5, X7))). 24.90/7.36 pC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), ','(mscE(X5, X7), mergeD(X6, X7, X8)))). 24.90/7.36 msE(.(X1, .(X2, X3)), X4) :- pC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X1, X5)) :- lessF(X1, X3). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X1, X5)) :- ','(lesscF(X1, X3), mergeD(X2, .(X3, X4), X5)). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X3, X5)) :- lessG(X3, X1). 24.90/7.36 mergeD(.(X1, X2), .(X3, X4), .(X3, X5)) :- ','(lesscG(X3, X1), mergeD(.(X1, X2), X4, X5)). 24.90/7.36 lessG(s(X1), s(X2)) :- lessG(X1, X2). 24.90/7.36 msH(X1, .(X2, X3), X4) :- pC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 lessF(s(X1), X2) :- lessG(X1, X2). 24.90/7.36 pJ(X1, X2, X3, X4, X5) :- lessF(X1, X2). 24.90/7.36 pJ(X1, X2, .(X3, X4), X5, .(X3, X6)) :- ','(lesscF(X1, X2), pJ(X3, X2, X4, X5, X6)). 24.90/7.36 pJ(X1, X2, .(X3, X4), X5, .(X2, X6)) :- ','(lesscF(X1, X2), pK(X2, X3, X4, X5, X6)). 24.90/7.36 pK(X1, X2, X3, X4, X5) :- lessG(X1, X2). 24.90/7.36 pK(X1, X2, X3, .(X4, X5), .(X2, X6)) :- ','(lesscG(X1, X2), pJ(X2, X4, X3, X5, X6)). 24.90/7.36 pK(X1, X2, X3, .(X4, X5), .(X4, X6)) :- ','(lesscG(X1, X2), pK(X4, X2, X3, X5, X6)). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- splitB(X2, X3, X4, X5). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- ','(splitcB(X2, X3, X4, X5), msH(X1, X5, X6)). 24.90/7.36 msL(.(X1, .(X2, X3)), []) :- ','(splitcB(X2, X3, X4, X5), ','(mscH(X1, X5, X6), msE(X4, X7))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- splitB(X2, X3, X5, X6). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), msH(X1, X6, X7)). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, X7), msE(X5, X8))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X4, X7)), ','(mscE(X5, .(X8, X9)), lessF(X4, X8)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, [])) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, .(X7, X8)), ','(mscE(X5, .(X4, X9)), lessG(X4, X7)))). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- splitB(X2, X3, X5, X6). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- ','(splitcB(X2, X3, X5, X6), msH(X1, X6, X7)). 24.90/7.36 msL(.(X1, .(X2, X3)), X4) :- ','(splitcB(X2, X3, X5, X6), ','(mscH(X1, X6, X7), msE(X5, X8))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, X5)) :- ','(splitcB(X2, X3, X6, X7), ','(mscH(X1, X7, .(X4, X8)), ','(mscE(X6, .(X9, X10)), lessF(X4, X9)))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, .(X5, X6))) :- ','(splitcB(X2, X3, X7, X8), ','(mscH(X1, X8, .(X4, .(X5, X9))), ','(mscE(X7, .(X10, X11)), ','(lesscF(X4, X10), pJ(X5, X10, X9, X11, X6))))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, .(X5, X6))) :- ','(splitcB(X2, X3, X7, X8), ','(mscH(X1, X8, .(X4, .(X9, X10))), ','(mscE(X7, .(X5, X11)), ','(lesscF(X4, X5), pK(X5, X9, X10, X11, X6))))). 24.90/7.36 msL(.(X1, .(X2, X3)), .(X4, X5)) :- ','(splitcB(X2, X3, X6, X7), ','(mscH(X1, X7, .(X8, X9)), ','(mscE(X6, .(X4, X10)), pK(X4, X8, X9, X10, X5)))). 24.90/7.36 24.90/7.36 Clauses: 24.90/7.36 24.90/7.36 splitcA([], [], []). 24.90/7.36 splitcA(.(X1, X2), .(X1, X3), X4) :- splitcA(X2, X4, X3). 24.90/7.36 splitcB(X1, X2, .(X1, X3), X4) :- splitcA(X2, X4, X3). 24.90/7.36 qcC(X1, X2, X3, X4, X5, X6, X7, X8) :- ','(splitcB(X1, .(X2, X3), X4, X5), ','(mscE(X4, X6), ','(mscE(X5, X7), mergecD(X6, X7, X8)))). 24.90/7.36 mscE([], []). 24.90/7.36 mscE(.(X1, []), .(X1, [])). 24.90/7.36 mscE(.(X1, .(X2, X3)), X4) :- qcC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 mergecD([], X1, X1). 24.90/7.36 mergecD(X1, [], X1). 24.90/7.36 mergecD(.(X1, X2), .(X3, X4), .(X1, X5)) :- ','(lesscF(X1, X3), mergecD(X2, .(X3, X4), X5)). 24.90/7.36 mergecD(.(X1, X2), .(X3, X4), .(X3, X5)) :- ','(lesscG(X3, X1), mergecD(.(X1, X2), X4, X5)). 24.90/7.36 lesscG(0, s(X1)). 24.90/7.36 lesscG(s(X1), s(X2)) :- lesscG(X1, X2). 24.90/7.36 mscH(X1, [], .(X1, [])). 24.90/7.36 mscH(X1, .(X2, X3), X4) :- qcC(X1, X2, X3, X5, X6, X7, X8, X4). 24.90/7.36 lesscF(0, X1). 24.90/7.36 lesscF(s(X1), X2) :- lesscG(X1, X2). 24.90/7.36 mergecI([], []). 24.90/7.36 mergecI([], []). 24.90/7.36 qcJ(X1, X2, [], X3, .(X2, X3)) :- lesscF(X1, X2). 24.90/7.36 qcJ(X1, X2, .(X3, X4), X5, .(X3, X6)) :- ','(lesscF(X1, X2), qcJ(X3, X2, X4, X5, X6)). 24.90/7.36 qcJ(X1, X2, .(X3, X4), X5, .(X2, X6)) :- ','(lesscF(X1, X2), qcK(X2, X3, X4, X5, X6)). 24.90/7.36 qcK(X1, X2, X3, [], .(X2, X3)) :- lesscG(X1, X2). 24.90/7.36 qcK(X1, X2, X3, .(X4, X5), .(X2, X6)) :- ','(lesscG(X1, X2), qcJ(X2, X4, X3, X5, X6)). 24.90/7.36 qcK(X1, X2, X3, .(X4, X5), .(X4, X6)) :- ','(lesscG(X1, X2), qcK(X4, X2, X3, X5, X6)). 24.90/7.36 24.90/7.36 Afs: 24.90/7.36 24.90/7.36 msL(x1, x2) = msL(x2) 24.90/7.36 24.90/7.36 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (119) TriplesToPiDPProof (SOUND) 24.90/7.36 We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: 24.90/7.36 24.90/7.36 msL_in_2: (f,b) 24.90/7.36 24.90/7.36 splitB_in_4: (f,f,f,f) 24.90/7.36 24.90/7.36 splitA_in_3: (f,f,f) 24.90/7.36 24.90/7.36 splitcB_in_4: (f,f,f,f) 24.90/7.36 24.90/7.36 splitcA_in_3: (f,f,f) 24.90/7.36 24.90/7.36 msH_in_3: (f,f,f) 24.90/7.36 24.90/7.36 pC_in_8: (f,f,f,f,f,f,f,f) 24.90/7.36 24.90/7.36 msE_in_2: (f,f) 24.90/7.36 24.90/7.36 mscE_in_2: (f,f) 24.90/7.36 24.90/7.36 qcC_in_8: (f,f,f,f,f,f,f,f) 24.90/7.36 24.90/7.36 mergecD_in_3: (f,f,f) 24.90/7.36 24.90/7.36 lesscF_in_2: (f,f) (b,f) (b,b) 24.90/7.36 24.90/7.36 lesscG_in_2: (f,f) (b,b) (b,f) 24.90/7.36 24.90/7.36 mergeD_in_3: (f,f,f) 24.90/7.36 24.90/7.36 lessF_in_2: (f,f) (b,f) 24.90/7.36 24.90/7.36 lessG_in_2: (f,f) (b,f) 24.90/7.36 24.90/7.36 mscH_in_3: (f,f,f) 24.90/7.36 24.90/7.36 pK_in_5: (b,f,f,f,b) 24.90/7.36 24.90/7.36 pJ_in_5: (b,f,f,f,b) 24.90/7.36 24.90/7.36 Transforming TRIPLES into the following Term Rewriting System: 24.90/7.36 24.90/7.36 Pi DP problem: 24.90/7.36 The TRS P consists of the following rules: 24.90/7.36 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> U30_AG(X1, X2, X3, splitB_in_aaaa(X2, X3, X4, X5)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> SPLITB_IN_AAAA(X2, X3, X4, X5) 24.90/7.36 SPLITB_IN_AAAA(X1, X2, .(X1, X3), X4) -> U2_AAAA(X1, X2, X3, X4, splitA_in_aaa(X2, X4, X3)) 24.90/7.36 SPLITB_IN_AAAA(X1, X2, .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.36 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> U1_AAA(X1, X2, X3, X4, splitA_in_aaa(X2, X4, X3)) 24.90/7.36 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> U31_AG(X1, X2, X3, splitcB_in_aaaa(X2, X3, X4, X5)) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> U32_AG(X1, X2, X3, msH_in_aaa(X1, X5, X6)) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> MSH_IN_AAA(X1, X5, X6) 24.90/7.36 MSH_IN_AAA(X1, .(X2, X3), X4) -> U18_AAA(X1, X2, X3, X4, pC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 MSH_IN_AAA(X1, .(X2, X3), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U3_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> SPLITB_IN_AAAA(X1, .(X2, X3), X4, X5) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U5_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, msE_in_aa(X4, X6)) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> MSE_IN_AA(X4, X6) 24.90/7.36 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> U10_AA(X1, X2, X3, X4, pC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U7_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, msE_in_aa(X5, X7)) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> MSE_IN_AA(X5, X7) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.36 U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U9_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mergeD_in_aaa(X6, X7, X8)) 24.90/7.36 U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> MERGED_IN_AAA(X6, X7, X8) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U11_AAA(X1, X2, X3, X4, X5, lessF_in_aa(X1, X3)) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> LESSF_IN_AA(X1, X3) 24.90/7.36 LESSF_IN_AA(s(X1), X2) -> U19_AA(X1, X2, lessG_in_aa(X1, X2)) 24.90/7.36 LESSF_IN_AA(s(X1), X2) -> LESSG_IN_AA(X1, X2) 24.90/7.36 LESSG_IN_AA(s(X1), s(X2)) -> U17_AA(X1, X2, lessG_in_aa(X1, X2)) 24.90/7.36 LESSG_IN_AA(s(X1), s(X2)) -> LESSG_IN_AA(X1, X2) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U12_AAA(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.36 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U13_AAA(X1, X2, X3, X4, X5, mergeD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.36 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> MERGED_IN_AAA(X2, .(X3, X4), X5) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U14_AAA(X1, X2, X3, X4, X5, lessG_in_aa(X3, X1)) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> LESSG_IN_AA(X3, X1) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U15_AAA(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.36 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U16_AAA(X1, X2, X3, X4, X5, mergeD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.36 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> MERGED_IN_AAA(.(X1, X2), X4, X5) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> U33_AG(X1, X2, X3, X4, mscH_in_aaa(X1, X5, X6)) 24.90/7.36 U33_AG(X1, X2, X3, X4, mscH_out_aaa(X1, X5, X6)) -> U34_AG(X1, X2, X3, msE_in_aa(X4, X7)) 24.90/7.36 U33_AG(X1, X2, X3, X4, mscH_out_aaa(X1, X5, X6)) -> MSE_IN_AA(X4, X7) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> U35_AG(X1, X2, X3, X4, splitB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> SPLITB_IN_AAAA(X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> U36_AG(X1, X2, X3, X4, splitcB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U37_AG(X1, X2, X3, X4, msH_in_aaa(X1, X6, X7)) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> MSH_IN_AAA(X1, X6, X7) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U38_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, X7)) 24.90/7.36 U38_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> U39_AG(X1, X2, X3, X4, msE_in_aa(X5, X8)) 24.90/7.36 U38_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> MSE_IN_AA(X5, X8) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U40_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, .(X4, X7))) 24.90/7.36 U40_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, .(X4, X7))) -> U41_AG(X1, X2, X3, X4, mscE_in_aa(X5, .(X8, X9))) 24.90/7.36 U41_AG(X1, X2, X3, X4, mscE_out_aa(X5, .(X8, X9))) -> U42_AG(X1, X2, X3, X4, lessF_in_ga(X4, X8)) 24.90/7.36 U41_AG(X1, X2, X3, X4, mscE_out_aa(X5, .(X8, X9))) -> LESSF_IN_GA(X4, X8) 24.90/7.36 LESSF_IN_GA(s(X1), X2) -> U19_GA(X1, X2, lessG_in_ga(X1, X2)) 24.90/7.36 LESSF_IN_GA(s(X1), X2) -> LESSG_IN_GA(X1, X2) 24.90/7.36 LESSG_IN_GA(s(X1), s(X2)) -> U17_GA(X1, X2, lessG_in_ga(X1, X2)) 24.90/7.36 LESSG_IN_GA(s(X1), s(X2)) -> LESSG_IN_GA(X1, X2) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U43_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, .(X7, X8))) 24.90/7.36 U43_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, .(X7, X8))) -> U44_AG(X1, X2, X3, X4, X7, mscE_in_aa(X5, .(X4, X9))) 24.90/7.36 U44_AG(X1, X2, X3, X4, X7, mscE_out_aa(X5, .(X4, X9))) -> U45_AG(X1, X2, X3, X4, lessG_in_ga(X4, X7)) 24.90/7.36 U44_AG(X1, X2, X3, X4, X7, mscE_out_aa(X5, .(X4, X9))) -> LESSG_IN_GA(X4, X7) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> U46_AG(X1, X2, X3, X4, splitB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> SPLITB_IN_AAAA(X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> U47_AG(X1, X2, X3, X4, splitcB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U48_AG(X1, X2, X3, X4, msH_in_aaa(X1, X6, X7)) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> MSH_IN_AAA(X1, X6, X7) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U49_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, X7)) 24.90/7.36 U49_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> U50_AG(X1, X2, X3, X4, msE_in_aa(X5, X8)) 24.90/7.36 U49_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> MSE_IN_AA(X5, X8) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, X5)) -> U51_AG(X1, X2, X3, X4, X5, splitcB_in_aaaa(X2, X3, X6, X7)) 24.90/7.36 U51_AG(X1, X2, X3, X4, X5, splitcB_out_aaaa(X2, X3, X6, X7)) -> U52_AG(X1, X2, X3, X4, X5, X6, mscH_in_aaa(X1, X7, .(X4, X8))) 24.90/7.36 U52_AG(X1, X2, X3, X4, X5, X6, mscH_out_aaa(X1, X7, .(X4, X8))) -> U53_AG(X1, X2, X3, X4, X5, mscE_in_aa(X6, .(X9, X10))) 24.90/7.36 U53_AG(X1, X2, X3, X4, X5, mscE_out_aa(X6, .(X9, X10))) -> U54_AG(X1, X2, X3, X4, X5, lessF_in_ga(X4, X9)) 24.90/7.36 U53_AG(X1, X2, X3, X4, X5, mscE_out_aa(X6, .(X9, X10))) -> LESSF_IN_GA(X4, X9) 24.90/7.36 U51_AG(X1, X2, X3, X4, X5, splitcB_out_aaaa(X2, X3, X6, X7)) -> U55_AG(X1, X2, X3, X4, X5, X6, mscH_in_aaa(X1, X7, .(X8, X9))) 24.90/7.36 U55_AG(X1, X2, X3, X4, X5, X6, mscH_out_aaa(X1, X7, .(X8, X9))) -> U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_in_aa(X6, .(X4, X10))) 24.90/7.36 U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_out_aa(X6, .(X4, X10))) -> U57_AG(X1, X2, X3, X4, X5, pK_in_gaaag(X4, X8, X9, X10, X5)) 24.90/7.36 U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_out_aa(X6, .(X4, X10))) -> PK_IN_GAAAG(X4, X8, X9, X10, X5) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, X4, X5) -> U25_GAAAG(X1, X2, X3, X4, X5, lessG_in_ga(X1, X2)) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, X4, X5) -> LESSG_IN_GA(X1, X2) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X2, X6)) -> U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_gg(X1, X2)) 24.90/7.36 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> U27_GAAAG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X2, X4, X3, X5, X6)) 24.90/7.36 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X4, X3, X5, X6) 24.90/7.36 PJ_IN_GAAAG(X1, X2, X3, X4, X5) -> U20_GAAAG(X1, X2, X3, X4, X5, lessF_in_ga(X1, X2)) 24.90/7.36 PJ_IN_GAAAG(X1, X2, X3, X4, X5) -> LESSF_IN_GA(X1, X2) 24.90/7.36 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X3, X6)) -> U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_ga(X1, X2)) 24.90/7.36 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> U22_GAAAG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X3, X2, X4, X5, X6)) 24.90/7.36 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> PJ_IN_GAAAG(X3, X2, X4, X5, X6) 24.90/7.36 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X2, X6)) -> U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_gg(X1, X2)) 24.90/7.36 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> U24_GAAAG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X2, X3, X4, X5, X6)) 24.90/7.36 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X3, X4, X5, X6) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X4, X6)) -> U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_ga(X1, X2)) 24.90/7.36 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> U29_GAAAG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X4, X2, X3, X5, X6)) 24.90/7.36 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> PK_IN_GAAAG(X4, X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, .(X5, X6))) -> U58_AG(X1, X2, X3, X4, X5, X6, splitcB_in_aaaa(X2, X3, X7, X8)) 24.90/7.36 U58_AG(X1, X2, X3, X4, X5, X6, splitcB_out_aaaa(X2, X3, X7, X8)) -> U59_AG(X1, X2, X3, X4, X5, X6, X7, mscH_in_aaa(X1, X8, .(X4, .(X5, X9)))) 24.90/7.36 U59_AG(X1, X2, X3, X4, X5, X6, X7, mscH_out_aaa(X1, X8, .(X4, .(X5, X9)))) -> U60_AG(X1, X2, X3, X4, X5, X6, X9, mscE_in_aa(X7, .(X10, X11))) 24.90/7.36 U60_AG(X1, X2, X3, X4, X5, X6, X9, mscE_out_aa(X7, .(X10, X11))) -> U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_in_ga(X4, X10)) 24.90/7.36 U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_ga(X4, X10)) -> U62_AG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X5, X10, X9, X11, X6)) 24.90/7.36 U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_ga(X4, X10)) -> PJ_IN_GAAAG(X5, X10, X9, X11, X6) 24.90/7.36 U58_AG(X1, X2, X3, X4, X5, X6, splitcB_out_aaaa(X2, X3, X7, X8)) -> U63_AG(X1, X2, X3, X4, X5, X6, X7, mscH_in_aaa(X1, X8, .(X4, .(X9, X10)))) 24.90/7.36 U63_AG(X1, X2, X3, X4, X5, X6, X7, mscH_out_aaa(X1, X8, .(X4, .(X9, X10)))) -> U64_AG(X1, X2, X3, X4, X5, X6, X9, X10, mscE_in_aa(X7, .(X5, X11))) 24.90/7.36 U64_AG(X1, X2, X3, X4, X5, X6, X9, X10, mscE_out_aa(X7, .(X5, X11))) -> U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_in_gg(X4, X5)) 24.90/7.36 U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_gg(X4, X5)) -> U66_AG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X5, X9, X10, X11, X6)) 24.90/7.36 U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_gg(X4, X5)) -> PK_IN_GAAAG(X5, X9, X10, X11, X6) 24.90/7.36 24.90/7.36 The TRS R consists of the following rules: 24.90/7.36 24.90/7.36 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.36 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.36 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.36 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.36 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.36 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.36 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.36 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.36 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.36 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.36 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.36 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.36 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.36 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.36 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.36 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.36 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.36 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.36 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.36 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.36 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.36 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.36 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.36 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.36 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.36 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.36 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.36 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.36 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.36 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.36 24.90/7.36 The argument filtering Pi contains the following mapping: 24.90/7.36 [] = [] 24.90/7.36 24.90/7.36 splitB_in_aaaa(x1, x2, x3, x4) = splitB_in_aaaa 24.90/7.36 24.90/7.36 splitA_in_aaa(x1, x2, x3) = splitA_in_aaa 24.90/7.36 24.90/7.36 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.36 24.90/7.36 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.36 24.90/7.36 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.36 24.90/7.36 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.36 24.90/7.36 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.36 24.90/7.36 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.36 24.90/7.36 msH_in_aaa(x1, x2, x3) = msH_in_aaa 24.90/7.36 24.90/7.36 pC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = pC_in_aaaaaaaa 24.90/7.36 24.90/7.36 msE_in_aa(x1, x2) = msE_in_aa 24.90/7.36 24.90/7.36 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.36 24.90/7.36 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.36 24.90/7.36 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.36 24.90/7.36 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.36 24.90/7.36 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.36 24.90/7.36 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.36 24.90/7.36 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.36 24.90/7.36 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.36 24.90/7.36 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.36 24.90/7.36 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.36 24.90/7.36 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.36 24.90/7.36 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.36 24.90/7.36 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.36 24.90/7.36 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.36 24.90/7.36 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.36 24.90/7.36 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.36 24.90/7.36 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.36 24.90/7.36 mergeD_in_aaa(x1, x2, x3) = mergeD_in_aaa 24.90/7.36 24.90/7.36 lessF_in_aa(x1, x2) = lessF_in_aa 24.90/7.36 24.90/7.36 lessG_in_aa(x1, x2) = lessG_in_aa 24.90/7.36 24.90/7.36 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.36 24.90/7.36 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.36 24.90/7.36 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.36 24.90/7.36 .(x1, x2) = .(x1, x2) 24.90/7.36 24.90/7.36 lessF_in_ga(x1, x2) = lessF_in_ga(x1) 24.90/7.36 24.90/7.36 s(x1) = s(x1) 24.90/7.36 24.90/7.36 lessG_in_ga(x1, x2) = lessG_in_ga(x1) 24.90/7.36 24.90/7.36 pK_in_gaaag(x1, x2, x3, x4, x5) = pK_in_gaaag(x1, x5) 24.90/7.36 24.90/7.36 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.36 24.90/7.36 0 = 0 24.90/7.36 24.90/7.36 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.36 24.90/7.36 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.36 24.90/7.36 pJ_in_gaaag(x1, x2, x3, x4, x5) = pJ_in_gaaag(x1, x5) 24.90/7.36 24.90/7.36 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.36 24.90/7.36 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.36 24.90/7.36 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.36 24.90/7.36 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.36 24.90/7.36 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.36 24.90/7.36 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.36 24.90/7.36 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.36 24.90/7.36 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.36 24.90/7.36 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.36 24.90/7.36 MSL_IN_AG(x1, x2) = MSL_IN_AG(x2) 24.90/7.36 24.90/7.36 U30_AG(x1, x2, x3, x4) = U30_AG(x4) 24.90/7.36 24.90/7.36 SPLITB_IN_AAAA(x1, x2, x3, x4) = SPLITB_IN_AAAA 24.90/7.36 24.90/7.36 U2_AAAA(x1, x2, x3, x4, x5) = U2_AAAA(x5) 24.90/7.36 24.90/7.36 SPLITA_IN_AAA(x1, x2, x3) = SPLITA_IN_AAA 24.90/7.36 24.90/7.36 U1_AAA(x1, x2, x3, x4, x5) = U1_AAA(x5) 24.90/7.36 24.90/7.36 U31_AG(x1, x2, x3, x4) = U31_AG(x4) 24.90/7.36 24.90/7.36 U32_AG(x1, x2, x3, x4) = U32_AG(x4) 24.90/7.36 24.90/7.36 MSH_IN_AAA(x1, x2, x3) = MSH_IN_AAA 24.90/7.36 24.90/7.36 U18_AAA(x1, x2, x3, x4, x5) = U18_AAA(x5) 24.90/7.36 24.90/7.36 PC_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = PC_IN_AAAAAAAA 24.90/7.36 24.90/7.36 U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U3_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U5_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 MSE_IN_AA(x1, x2) = MSE_IN_AA 24.90/7.36 24.90/7.36 U10_AA(x1, x2, x3, x4, x5) = U10_AA(x5) 24.90/7.36 24.90/7.36 U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U7_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U8_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U9_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 MERGED_IN_AAA(x1, x2, x3) = MERGED_IN_AAA 24.90/7.36 24.90/7.36 U11_AAA(x1, x2, x3, x4, x5, x6) = U11_AAA(x6) 24.90/7.36 24.90/7.36 LESSF_IN_AA(x1, x2) = LESSF_IN_AA 24.90/7.36 24.90/7.36 U19_AA(x1, x2, x3) = U19_AA(x3) 24.90/7.36 24.90/7.36 LESSG_IN_AA(x1, x2) = LESSG_IN_AA 24.90/7.36 24.90/7.36 U17_AA(x1, x2, x3) = U17_AA(x3) 24.90/7.36 24.90/7.36 U12_AAA(x1, x2, x3, x4, x5, x6) = U12_AAA(x6) 24.90/7.36 24.90/7.36 U13_AAA(x1, x2, x3, x4, x5, x6) = U13_AAA(x6) 24.90/7.36 24.90/7.36 U14_AAA(x1, x2, x3, x4, x5, x6) = U14_AAA(x6) 24.90/7.36 24.90/7.36 U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6) 24.90/7.36 24.90/7.36 U16_AAA(x1, x2, x3, x4, x5, x6) = U16_AAA(x6) 24.90/7.36 24.90/7.36 U33_AG(x1, x2, x3, x4, x5) = U33_AG(x5) 24.90/7.36 24.90/7.36 U34_AG(x1, x2, x3, x4) = U34_AG(x4) 24.90/7.36 24.90/7.36 U35_AG(x1, x2, x3, x4, x5) = U35_AG(x4, x5) 24.90/7.36 24.90/7.36 U36_AG(x1, x2, x3, x4, x5) = U36_AG(x4, x5) 24.90/7.36 24.90/7.36 U37_AG(x1, x2, x3, x4, x5) = U37_AG(x4, x5) 24.90/7.36 24.90/7.36 U38_AG(x1, x2, x3, x4, x5, x6) = U38_AG(x4, x6) 24.90/7.36 24.90/7.36 U39_AG(x1, x2, x3, x4, x5) = U39_AG(x4, x5) 24.90/7.36 24.90/7.36 U40_AG(x1, x2, x3, x4, x5, x6) = U40_AG(x4, x6) 24.90/7.36 24.90/7.36 U41_AG(x1, x2, x3, x4, x5) = U41_AG(x4, x5) 24.90/7.36 24.90/7.36 U42_AG(x1, x2, x3, x4, x5) = U42_AG(x4, x5) 24.90/7.36 24.90/7.36 LESSF_IN_GA(x1, x2) = LESSF_IN_GA(x1) 24.90/7.36 24.90/7.36 U19_GA(x1, x2, x3) = U19_GA(x1, x3) 24.90/7.36 24.90/7.36 LESSG_IN_GA(x1, x2) = LESSG_IN_GA(x1) 24.90/7.36 24.90/7.36 U17_GA(x1, x2, x3) = U17_GA(x1, x3) 24.90/7.36 24.90/7.36 U43_AG(x1, x2, x3, x4, x5, x6) = U43_AG(x4, x6) 24.90/7.36 24.90/7.36 U44_AG(x1, x2, x3, x4, x5, x6) = U44_AG(x4, x6) 24.90/7.36 24.90/7.36 U45_AG(x1, x2, x3, x4, x5) = U45_AG(x4, x5) 24.90/7.36 24.90/7.36 U46_AG(x1, x2, x3, x4, x5) = U46_AG(x4, x5) 24.90/7.36 24.90/7.36 U47_AG(x1, x2, x3, x4, x5) = U47_AG(x4, x5) 24.90/7.36 24.90/7.36 U48_AG(x1, x2, x3, x4, x5) = U48_AG(x4, x5) 24.90/7.36 24.90/7.36 U49_AG(x1, x2, x3, x4, x5, x6) = U49_AG(x4, x6) 24.90/7.36 24.90/7.36 U50_AG(x1, x2, x3, x4, x5) = U50_AG(x4, x5) 24.90/7.36 24.90/7.36 U51_AG(x1, x2, x3, x4, x5, x6) = U51_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U52_AG(x1, x2, x3, x4, x5, x6, x7) = U52_AG(x4, x5, x7) 24.90/7.36 24.90/7.36 U53_AG(x1, x2, x3, x4, x5, x6) = U53_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U54_AG(x1, x2, x3, x4, x5, x6) = U54_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U55_AG(x1, x2, x3, x4, x5, x6, x7) = U55_AG(x4, x5, x7) 24.90/7.36 24.90/7.36 U56_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U56_AG(x4, x5, x8) 24.90/7.36 24.90/7.36 U57_AG(x1, x2, x3, x4, x5, x6) = U57_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 PK_IN_GAAAG(x1, x2, x3, x4, x5) = PK_IN_GAAAG(x1, x5) 24.90/7.36 24.90/7.36 U25_GAAAG(x1, x2, x3, x4, x5, x6) = U25_GAAAG(x1, x5, x6) 24.90/7.36 24.90/7.36 U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U27_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U27_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 PJ_IN_GAAAG(x1, x2, x3, x4, x5) = PJ_IN_GAAAG(x1, x5) 24.90/7.36 24.90/7.36 U20_GAAAG(x1, x2, x3, x4, x5, x6) = U20_GAAAG(x1, x5, x6) 24.90/7.36 24.90/7.36 U21_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U21_GAAAG(x1, x3, x6, x7) 24.90/7.36 24.90/7.36 U22_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U22_GAAAG(x1, x3, x6, x7) 24.90/7.36 24.90/7.36 U23_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U23_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U24_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U24_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U28_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U28_GAAAG(x1, x4, x6, x7) 24.90/7.36 24.90/7.36 U29_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U29_GAAAG(x1, x4, x6, x7) 24.90/7.36 24.90/7.36 U58_AG(x1, x2, x3, x4, x5, x6, x7) = U58_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 U59_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U59_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U60_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U60_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U61_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U61_AG(x4, x5, x6, x10) 24.90/7.36 24.90/7.36 U62_AG(x1, x2, x3, x4, x5, x6, x7) = U62_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 U63_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U63_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U64_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U64_AG(x4, x5, x6, x9) 24.90/7.36 24.90/7.36 U65_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U65_AG(x4, x5, x6, x10) 24.90/7.36 24.90/7.36 U66_AG(x1, x2, x3, x4, x5, x6, x7) = U66_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 24.90/7.36 We have to consider all (P,R,Pi)-chains 24.90/7.36 24.90/7.36 24.90/7.36 Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES 24.90/7.36 24.90/7.36 24.90/7.36 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (120) 24.90/7.36 Obligation: 24.90/7.36 Pi DP problem: 24.90/7.36 The TRS P consists of the following rules: 24.90/7.36 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> U30_AG(X1, X2, X3, splitB_in_aaaa(X2, X3, X4, X5)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> SPLITB_IN_AAAA(X2, X3, X4, X5) 24.90/7.36 SPLITB_IN_AAAA(X1, X2, .(X1, X3), X4) -> U2_AAAA(X1, X2, X3, X4, splitA_in_aaa(X2, X4, X3)) 24.90/7.36 SPLITB_IN_AAAA(X1, X2, .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.36 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> U1_AAA(X1, X2, X3, X4, splitA_in_aaa(X2, X4, X3)) 24.90/7.36 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), []) -> U31_AG(X1, X2, X3, splitcB_in_aaaa(X2, X3, X4, X5)) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> U32_AG(X1, X2, X3, msH_in_aaa(X1, X5, X6)) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> MSH_IN_AAA(X1, X5, X6) 24.90/7.36 MSH_IN_AAA(X1, .(X2, X3), X4) -> U18_AAA(X1, X2, X3, X4, pC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 MSH_IN_AAA(X1, .(X2, X3), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U3_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> SPLITB_IN_AAAA(X1, .(X2, X3), X4, X5) 24.90/7.36 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U5_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, msE_in_aa(X4, X6)) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> MSE_IN_AA(X4, X6) 24.90/7.36 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> U10_AA(X1, X2, X3, X4, pC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.36 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U7_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, msE_in_aa(X5, X7)) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> MSE_IN_AA(X5, X7) 24.90/7.36 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.36 U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U9_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mergeD_in_aaa(X6, X7, X8)) 24.90/7.36 U8_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> MERGED_IN_AAA(X6, X7, X8) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U11_AAA(X1, X2, X3, X4, X5, lessF_in_aa(X1, X3)) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> LESSF_IN_AA(X1, X3) 24.90/7.36 LESSF_IN_AA(s(X1), X2) -> U19_AA(X1, X2, lessG_in_aa(X1, X2)) 24.90/7.36 LESSF_IN_AA(s(X1), X2) -> LESSG_IN_AA(X1, X2) 24.90/7.36 LESSG_IN_AA(s(X1), s(X2)) -> U17_AA(X1, X2, lessG_in_aa(X1, X2)) 24.90/7.36 LESSG_IN_AA(s(X1), s(X2)) -> LESSG_IN_AA(X1, X2) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U12_AAA(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.36 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U13_AAA(X1, X2, X3, X4, X5, mergeD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.36 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> MERGED_IN_AAA(X2, .(X3, X4), X5) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U14_AAA(X1, X2, X3, X4, X5, lessG_in_aa(X3, X1)) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> LESSG_IN_AA(X3, X1) 24.90/7.36 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U15_AAA(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.36 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U16_AAA(X1, X2, X3, X4, X5, mergeD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.36 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> MERGED_IN_AAA(.(X1, X2), X4, X5) 24.90/7.36 U31_AG(X1, X2, X3, splitcB_out_aaaa(X2, X3, X4, X5)) -> U33_AG(X1, X2, X3, X4, mscH_in_aaa(X1, X5, X6)) 24.90/7.36 U33_AG(X1, X2, X3, X4, mscH_out_aaa(X1, X5, X6)) -> U34_AG(X1, X2, X3, msE_in_aa(X4, X7)) 24.90/7.36 U33_AG(X1, X2, X3, X4, mscH_out_aaa(X1, X5, X6)) -> MSE_IN_AA(X4, X7) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> U35_AG(X1, X2, X3, X4, splitB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> SPLITB_IN_AAAA(X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, [])) -> U36_AG(X1, X2, X3, X4, splitcB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U37_AG(X1, X2, X3, X4, msH_in_aaa(X1, X6, X7)) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> MSH_IN_AAA(X1, X6, X7) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U38_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, X7)) 24.90/7.36 U38_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> U39_AG(X1, X2, X3, X4, msE_in_aa(X5, X8)) 24.90/7.36 U38_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> MSE_IN_AA(X5, X8) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U40_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, .(X4, X7))) 24.90/7.36 U40_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, .(X4, X7))) -> U41_AG(X1, X2, X3, X4, mscE_in_aa(X5, .(X8, X9))) 24.90/7.36 U41_AG(X1, X2, X3, X4, mscE_out_aa(X5, .(X8, X9))) -> U42_AG(X1, X2, X3, X4, lessF_in_ga(X4, X8)) 24.90/7.36 U41_AG(X1, X2, X3, X4, mscE_out_aa(X5, .(X8, X9))) -> LESSF_IN_GA(X4, X8) 24.90/7.36 LESSF_IN_GA(s(X1), X2) -> U19_GA(X1, X2, lessG_in_ga(X1, X2)) 24.90/7.36 LESSF_IN_GA(s(X1), X2) -> LESSG_IN_GA(X1, X2) 24.90/7.36 LESSG_IN_GA(s(X1), s(X2)) -> U17_GA(X1, X2, lessG_in_ga(X1, X2)) 24.90/7.36 LESSG_IN_GA(s(X1), s(X2)) -> LESSG_IN_GA(X1, X2) 24.90/7.36 U36_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U43_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, .(X7, X8))) 24.90/7.36 U43_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, .(X7, X8))) -> U44_AG(X1, X2, X3, X4, X7, mscE_in_aa(X5, .(X4, X9))) 24.90/7.36 U44_AG(X1, X2, X3, X4, X7, mscE_out_aa(X5, .(X4, X9))) -> U45_AG(X1, X2, X3, X4, lessG_in_ga(X4, X7)) 24.90/7.36 U44_AG(X1, X2, X3, X4, X7, mscE_out_aa(X5, .(X4, X9))) -> LESSG_IN_GA(X4, X7) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> U46_AG(X1, X2, X3, X4, splitB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> SPLITB_IN_AAAA(X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), X4) -> U47_AG(X1, X2, X3, X4, splitcB_in_aaaa(X2, X3, X5, X6)) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U48_AG(X1, X2, X3, X4, msH_in_aaa(X1, X6, X7)) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> MSH_IN_AAA(X1, X6, X7) 24.90/7.36 U47_AG(X1, X2, X3, X4, splitcB_out_aaaa(X2, X3, X5, X6)) -> U49_AG(X1, X2, X3, X4, X5, mscH_in_aaa(X1, X6, X7)) 24.90/7.36 U49_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> U50_AG(X1, X2, X3, X4, msE_in_aa(X5, X8)) 24.90/7.36 U49_AG(X1, X2, X3, X4, X5, mscH_out_aaa(X1, X6, X7)) -> MSE_IN_AA(X5, X8) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, X5)) -> U51_AG(X1, X2, X3, X4, X5, splitcB_in_aaaa(X2, X3, X6, X7)) 24.90/7.36 U51_AG(X1, X2, X3, X4, X5, splitcB_out_aaaa(X2, X3, X6, X7)) -> U52_AG(X1, X2, X3, X4, X5, X6, mscH_in_aaa(X1, X7, .(X4, X8))) 24.90/7.36 U52_AG(X1, X2, X3, X4, X5, X6, mscH_out_aaa(X1, X7, .(X4, X8))) -> U53_AG(X1, X2, X3, X4, X5, mscE_in_aa(X6, .(X9, X10))) 24.90/7.36 U53_AG(X1, X2, X3, X4, X5, mscE_out_aa(X6, .(X9, X10))) -> U54_AG(X1, X2, X3, X4, X5, lessF_in_ga(X4, X9)) 24.90/7.36 U53_AG(X1, X2, X3, X4, X5, mscE_out_aa(X6, .(X9, X10))) -> LESSF_IN_GA(X4, X9) 24.90/7.36 U51_AG(X1, X2, X3, X4, X5, splitcB_out_aaaa(X2, X3, X6, X7)) -> U55_AG(X1, X2, X3, X4, X5, X6, mscH_in_aaa(X1, X7, .(X8, X9))) 24.90/7.36 U55_AG(X1, X2, X3, X4, X5, X6, mscH_out_aaa(X1, X7, .(X8, X9))) -> U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_in_aa(X6, .(X4, X10))) 24.90/7.36 U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_out_aa(X6, .(X4, X10))) -> U57_AG(X1, X2, X3, X4, X5, pK_in_gaaag(X4, X8, X9, X10, X5)) 24.90/7.36 U56_AG(X1, X2, X3, X4, X5, X8, X9, mscE_out_aa(X6, .(X4, X10))) -> PK_IN_GAAAG(X4, X8, X9, X10, X5) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, X4, X5) -> U25_GAAAG(X1, X2, X3, X4, X5, lessG_in_ga(X1, X2)) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, X4, X5) -> LESSG_IN_GA(X1, X2) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X2, X6)) -> U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_gg(X1, X2)) 24.90/7.36 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> U27_GAAAG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X2, X4, X3, X5, X6)) 24.90/7.36 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X4, X3, X5, X6) 24.90/7.36 PJ_IN_GAAAG(X1, X2, X3, X4, X5) -> U20_GAAAG(X1, X2, X3, X4, X5, lessF_in_ga(X1, X2)) 24.90/7.36 PJ_IN_GAAAG(X1, X2, X3, X4, X5) -> LESSF_IN_GA(X1, X2) 24.90/7.36 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X3, X6)) -> U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_ga(X1, X2)) 24.90/7.36 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> U22_GAAAG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X3, X2, X4, X5, X6)) 24.90/7.36 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> PJ_IN_GAAAG(X3, X2, X4, X5, X6) 24.90/7.36 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X2, X6)) -> U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_gg(X1, X2)) 24.90/7.36 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> U24_GAAAG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X2, X3, X4, X5, X6)) 24.90/7.36 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X3, X4, X5, X6) 24.90/7.36 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X4, X6)) -> U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_ga(X1, X2)) 24.90/7.36 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> U29_GAAAG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X4, X2, X3, X5, X6)) 24.90/7.36 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> PK_IN_GAAAG(X4, X2, X3, X5, X6) 24.90/7.36 MSL_IN_AG(.(X1, .(X2, X3)), .(X4, .(X5, X6))) -> U58_AG(X1, X2, X3, X4, X5, X6, splitcB_in_aaaa(X2, X3, X7, X8)) 24.90/7.36 U58_AG(X1, X2, X3, X4, X5, X6, splitcB_out_aaaa(X2, X3, X7, X8)) -> U59_AG(X1, X2, X3, X4, X5, X6, X7, mscH_in_aaa(X1, X8, .(X4, .(X5, X9)))) 24.90/7.36 U59_AG(X1, X2, X3, X4, X5, X6, X7, mscH_out_aaa(X1, X8, .(X4, .(X5, X9)))) -> U60_AG(X1, X2, X3, X4, X5, X6, X9, mscE_in_aa(X7, .(X10, X11))) 24.90/7.36 U60_AG(X1, X2, X3, X4, X5, X6, X9, mscE_out_aa(X7, .(X10, X11))) -> U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_in_ga(X4, X10)) 24.90/7.36 U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_ga(X4, X10)) -> U62_AG(X1, X2, X3, X4, X5, X6, pJ_in_gaaag(X5, X10, X9, X11, X6)) 24.90/7.36 U61_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_ga(X4, X10)) -> PJ_IN_GAAAG(X5, X10, X9, X11, X6) 24.90/7.36 U58_AG(X1, X2, X3, X4, X5, X6, splitcB_out_aaaa(X2, X3, X7, X8)) -> U63_AG(X1, X2, X3, X4, X5, X6, X7, mscH_in_aaa(X1, X8, .(X4, .(X9, X10)))) 24.90/7.36 U63_AG(X1, X2, X3, X4, X5, X6, X7, mscH_out_aaa(X1, X8, .(X4, .(X9, X10)))) -> U64_AG(X1, X2, X3, X4, X5, X6, X9, X10, mscE_in_aa(X7, .(X5, X11))) 24.90/7.36 U64_AG(X1, X2, X3, X4, X5, X6, X9, X10, mscE_out_aa(X7, .(X5, X11))) -> U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_in_gg(X4, X5)) 24.90/7.36 U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_gg(X4, X5)) -> U66_AG(X1, X2, X3, X4, X5, X6, pK_in_gaaag(X5, X9, X10, X11, X6)) 24.90/7.36 U65_AG(X1, X2, X3, X4, X5, X6, X9, X10, X11, lesscF_out_gg(X4, X5)) -> PK_IN_GAAAG(X5, X9, X10, X11, X6) 24.90/7.36 24.90/7.36 The TRS R consists of the following rules: 24.90/7.36 24.90/7.36 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.36 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.36 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.36 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.36 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.36 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.36 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.36 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.36 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.36 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.36 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.36 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.36 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.36 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.36 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.36 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.36 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.36 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.36 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.36 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.36 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.36 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.36 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.36 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.36 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.36 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.36 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.36 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.36 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.36 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.36 24.90/7.36 The argument filtering Pi contains the following mapping: 24.90/7.36 [] = [] 24.90/7.36 24.90/7.36 splitB_in_aaaa(x1, x2, x3, x4) = splitB_in_aaaa 24.90/7.36 24.90/7.36 splitA_in_aaa(x1, x2, x3) = splitA_in_aaa 24.90/7.36 24.90/7.36 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.36 24.90/7.36 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.36 24.90/7.36 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.36 24.90/7.36 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.36 24.90/7.36 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.36 24.90/7.36 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.36 24.90/7.36 msH_in_aaa(x1, x2, x3) = msH_in_aaa 24.90/7.36 24.90/7.36 pC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = pC_in_aaaaaaaa 24.90/7.36 24.90/7.36 msE_in_aa(x1, x2) = msE_in_aa 24.90/7.36 24.90/7.36 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.36 24.90/7.36 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.36 24.90/7.36 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.36 24.90/7.36 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.36 24.90/7.36 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.36 24.90/7.36 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.36 24.90/7.36 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.36 24.90/7.36 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.36 24.90/7.36 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.36 24.90/7.36 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.36 24.90/7.36 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.36 24.90/7.36 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.36 24.90/7.36 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.36 24.90/7.36 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.36 24.90/7.36 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.36 24.90/7.36 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.36 24.90/7.36 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.36 24.90/7.36 mergeD_in_aaa(x1, x2, x3) = mergeD_in_aaa 24.90/7.36 24.90/7.36 lessF_in_aa(x1, x2) = lessF_in_aa 24.90/7.36 24.90/7.36 lessG_in_aa(x1, x2) = lessG_in_aa 24.90/7.36 24.90/7.36 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.36 24.90/7.36 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.36 24.90/7.36 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.36 24.90/7.36 .(x1, x2) = .(x1, x2) 24.90/7.36 24.90/7.36 lessF_in_ga(x1, x2) = lessF_in_ga(x1) 24.90/7.36 24.90/7.36 s(x1) = s(x1) 24.90/7.36 24.90/7.36 lessG_in_ga(x1, x2) = lessG_in_ga(x1) 24.90/7.36 24.90/7.36 pK_in_gaaag(x1, x2, x3, x4, x5) = pK_in_gaaag(x1, x5) 24.90/7.36 24.90/7.36 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.36 24.90/7.36 0 = 0 24.90/7.36 24.90/7.36 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.36 24.90/7.36 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.36 24.90/7.36 pJ_in_gaaag(x1, x2, x3, x4, x5) = pJ_in_gaaag(x1, x5) 24.90/7.36 24.90/7.36 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.36 24.90/7.36 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.36 24.90/7.36 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.36 24.90/7.36 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.36 24.90/7.36 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.36 24.90/7.36 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.36 24.90/7.36 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.36 24.90/7.36 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.36 24.90/7.36 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.36 24.90/7.36 MSL_IN_AG(x1, x2) = MSL_IN_AG(x2) 24.90/7.36 24.90/7.36 U30_AG(x1, x2, x3, x4) = U30_AG(x4) 24.90/7.36 24.90/7.36 SPLITB_IN_AAAA(x1, x2, x3, x4) = SPLITB_IN_AAAA 24.90/7.36 24.90/7.36 U2_AAAA(x1, x2, x3, x4, x5) = U2_AAAA(x5) 24.90/7.36 24.90/7.36 SPLITA_IN_AAA(x1, x2, x3) = SPLITA_IN_AAA 24.90/7.36 24.90/7.36 U1_AAA(x1, x2, x3, x4, x5) = U1_AAA(x5) 24.90/7.36 24.90/7.36 U31_AG(x1, x2, x3, x4) = U31_AG(x4) 24.90/7.36 24.90/7.36 U32_AG(x1, x2, x3, x4) = U32_AG(x4) 24.90/7.36 24.90/7.36 MSH_IN_AAA(x1, x2, x3) = MSH_IN_AAA 24.90/7.36 24.90/7.36 U18_AAA(x1, x2, x3, x4, x5) = U18_AAA(x5) 24.90/7.36 24.90/7.36 PC_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = PC_IN_AAAAAAAA 24.90/7.36 24.90/7.36 U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U3_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U5_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 MSE_IN_AA(x1, x2) = MSE_IN_AA 24.90/7.36 24.90/7.36 U10_AA(x1, x2, x3, x4, x5) = U10_AA(x5) 24.90/7.36 24.90/7.36 U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U7_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U8_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U9_AAAAAAAA(x9) 24.90/7.36 24.90/7.36 MERGED_IN_AAA(x1, x2, x3) = MERGED_IN_AAA 24.90/7.36 24.90/7.36 U11_AAA(x1, x2, x3, x4, x5, x6) = U11_AAA(x6) 24.90/7.36 24.90/7.36 LESSF_IN_AA(x1, x2) = LESSF_IN_AA 24.90/7.36 24.90/7.36 U19_AA(x1, x2, x3) = U19_AA(x3) 24.90/7.36 24.90/7.36 LESSG_IN_AA(x1, x2) = LESSG_IN_AA 24.90/7.36 24.90/7.36 U17_AA(x1, x2, x3) = U17_AA(x3) 24.90/7.36 24.90/7.36 U12_AAA(x1, x2, x3, x4, x5, x6) = U12_AAA(x6) 24.90/7.36 24.90/7.36 U13_AAA(x1, x2, x3, x4, x5, x6) = U13_AAA(x6) 24.90/7.36 24.90/7.36 U14_AAA(x1, x2, x3, x4, x5, x6) = U14_AAA(x6) 24.90/7.36 24.90/7.36 U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6) 24.90/7.36 24.90/7.36 U16_AAA(x1, x2, x3, x4, x5, x6) = U16_AAA(x6) 24.90/7.36 24.90/7.36 U33_AG(x1, x2, x3, x4, x5) = U33_AG(x5) 24.90/7.36 24.90/7.36 U34_AG(x1, x2, x3, x4) = U34_AG(x4) 24.90/7.36 24.90/7.36 U35_AG(x1, x2, x3, x4, x5) = U35_AG(x4, x5) 24.90/7.36 24.90/7.36 U36_AG(x1, x2, x3, x4, x5) = U36_AG(x4, x5) 24.90/7.36 24.90/7.36 U37_AG(x1, x2, x3, x4, x5) = U37_AG(x4, x5) 24.90/7.36 24.90/7.36 U38_AG(x1, x2, x3, x4, x5, x6) = U38_AG(x4, x6) 24.90/7.36 24.90/7.36 U39_AG(x1, x2, x3, x4, x5) = U39_AG(x4, x5) 24.90/7.36 24.90/7.36 U40_AG(x1, x2, x3, x4, x5, x6) = U40_AG(x4, x6) 24.90/7.36 24.90/7.36 U41_AG(x1, x2, x3, x4, x5) = U41_AG(x4, x5) 24.90/7.36 24.90/7.36 U42_AG(x1, x2, x3, x4, x5) = U42_AG(x4, x5) 24.90/7.36 24.90/7.36 LESSF_IN_GA(x1, x2) = LESSF_IN_GA(x1) 24.90/7.36 24.90/7.36 U19_GA(x1, x2, x3) = U19_GA(x1, x3) 24.90/7.36 24.90/7.36 LESSG_IN_GA(x1, x2) = LESSG_IN_GA(x1) 24.90/7.36 24.90/7.36 U17_GA(x1, x2, x3) = U17_GA(x1, x3) 24.90/7.36 24.90/7.36 U43_AG(x1, x2, x3, x4, x5, x6) = U43_AG(x4, x6) 24.90/7.36 24.90/7.36 U44_AG(x1, x2, x3, x4, x5, x6) = U44_AG(x4, x6) 24.90/7.36 24.90/7.36 U45_AG(x1, x2, x3, x4, x5) = U45_AG(x4, x5) 24.90/7.36 24.90/7.36 U46_AG(x1, x2, x3, x4, x5) = U46_AG(x4, x5) 24.90/7.36 24.90/7.36 U47_AG(x1, x2, x3, x4, x5) = U47_AG(x4, x5) 24.90/7.36 24.90/7.36 U48_AG(x1, x2, x3, x4, x5) = U48_AG(x4, x5) 24.90/7.36 24.90/7.36 U49_AG(x1, x2, x3, x4, x5, x6) = U49_AG(x4, x6) 24.90/7.36 24.90/7.36 U50_AG(x1, x2, x3, x4, x5) = U50_AG(x4, x5) 24.90/7.36 24.90/7.36 U51_AG(x1, x2, x3, x4, x5, x6) = U51_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U52_AG(x1, x2, x3, x4, x5, x6, x7) = U52_AG(x4, x5, x7) 24.90/7.36 24.90/7.36 U53_AG(x1, x2, x3, x4, x5, x6) = U53_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U54_AG(x1, x2, x3, x4, x5, x6) = U54_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 U55_AG(x1, x2, x3, x4, x5, x6, x7) = U55_AG(x4, x5, x7) 24.90/7.36 24.90/7.36 U56_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U56_AG(x4, x5, x8) 24.90/7.36 24.90/7.36 U57_AG(x1, x2, x3, x4, x5, x6) = U57_AG(x4, x5, x6) 24.90/7.36 24.90/7.36 PK_IN_GAAAG(x1, x2, x3, x4, x5) = PK_IN_GAAAG(x1, x5) 24.90/7.36 24.90/7.36 U25_GAAAG(x1, x2, x3, x4, x5, x6) = U25_GAAAG(x1, x5, x6) 24.90/7.36 24.90/7.36 U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U27_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U27_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 PJ_IN_GAAAG(x1, x2, x3, x4, x5) = PJ_IN_GAAAG(x1, x5) 24.90/7.36 24.90/7.36 U20_GAAAG(x1, x2, x3, x4, x5, x6) = U20_GAAAG(x1, x5, x6) 24.90/7.36 24.90/7.36 U21_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U21_GAAAG(x1, x3, x6, x7) 24.90/7.36 24.90/7.36 U22_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U22_GAAAG(x1, x3, x6, x7) 24.90/7.36 24.90/7.36 U23_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U23_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U24_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U24_GAAAG(x1, x2, x6, x7) 24.90/7.36 24.90/7.36 U28_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U28_GAAAG(x1, x4, x6, x7) 24.90/7.36 24.90/7.36 U29_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U29_GAAAG(x1, x4, x6, x7) 24.90/7.36 24.90/7.36 U58_AG(x1, x2, x3, x4, x5, x6, x7) = U58_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 U59_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U59_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U60_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U60_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U61_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U61_AG(x4, x5, x6, x10) 24.90/7.36 24.90/7.36 U62_AG(x1, x2, x3, x4, x5, x6, x7) = U62_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 U63_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U63_AG(x4, x5, x6, x8) 24.90/7.36 24.90/7.36 U64_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U64_AG(x4, x5, x6, x9) 24.90/7.36 24.90/7.36 U65_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U65_AG(x4, x5, x6, x10) 24.90/7.36 24.90/7.36 U66_AG(x1, x2, x3, x4, x5, x6, x7) = U66_AG(x4, x5, x6, x7) 24.90/7.36 24.90/7.36 24.90/7.36 We have to consider all (P,R,Pi)-chains 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (121) DependencyGraphProof (EQUIVALENT) 24.90/7.36 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 85 less nodes. 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (122) 24.90/7.36 Complex Obligation (AND) 24.90/7.36 24.90/7.36 ---------------------------------------- 24.90/7.36 24.90/7.36 (123) 24.90/7.36 Obligation: 24.90/7.36 Pi DP problem: 24.90/7.36 The TRS P consists of the following rules: 24.90/7.36 24.90/7.36 LESSG_IN_GA(s(X1), s(X2)) -> LESSG_IN_GA(X1, X2) 24.90/7.36 24.90/7.36 The TRS R consists of the following rules: 24.90/7.36 24.90/7.36 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.36 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.36 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.36 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.36 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.36 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.36 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.36 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.36 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.36 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.36 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.36 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.36 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.36 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.36 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.36 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.36 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.36 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.36 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.36 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.36 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.36 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.36 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.36 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.36 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.36 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.36 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.36 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.36 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.36 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.36 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.36 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.36 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.36 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.36 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.36 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.36 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.36 24.90/7.36 The argument filtering Pi contains the following mapping: 24.90/7.36 [] = [] 24.90/7.36 24.90/7.36 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.36 24.90/7.36 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.36 24.90/7.36 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.36 24.90/7.36 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.36 24.90/7.36 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.36 24.90/7.36 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.36 24.90/7.36 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.36 24.90/7.36 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.36 24.90/7.36 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.36 24.90/7.36 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.36 24.90/7.36 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.36 24.90/7.36 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.36 24.90/7.36 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.36 24.90/7.36 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.36 24.90/7.36 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.36 24.90/7.36 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.36 24.90/7.36 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.36 24.90/7.36 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.36 24.90/7.36 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.36 24.90/7.36 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.36 24.90/7.36 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.36 24.90/7.36 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.36 24.90/7.36 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.36 24.90/7.36 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.36 24.90/7.36 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.36 24.90/7.36 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.36 24.90/7.36 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.36 24.90/7.36 .(x1, x2) = .(x1, x2) 24.90/7.36 24.90/7.36 s(x1) = s(x1) 24.90/7.36 24.90/7.36 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 LESSG_IN_GA(x1, x2) = LESSG_IN_GA(x1) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (124) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (125) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 LESSG_IN_GA(s(X1), s(X2)) -> LESSG_IN_GA(X1, X2) 24.90/7.37 24.90/7.37 R is empty. 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 LESSG_IN_GA(x1, x2) = LESSG_IN_GA(x1) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (126) PiDPToQDPProof (SOUND) 24.90/7.37 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (127) 24.90/7.37 Obligation: 24.90/7.37 Q DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 LESSG_IN_GA(s(X1)) -> LESSG_IN_GA(X1) 24.90/7.37 24.90/7.37 R is empty. 24.90/7.37 Q is empty. 24.90/7.37 We have to consider all (P,Q,R)-chains. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (128) QDPSizeChangeProof (EQUIVALENT) 24.90/7.37 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. 24.90/7.37 24.90/7.37 From the DPs we obtained the following set of size-change graphs: 24.90/7.37 *LESSG_IN_GA(s(X1)) -> LESSG_IN_GA(X1) 24.90/7.37 The graph contains the following edges 1 > 1 24.90/7.37 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (129) 24.90/7.37 YES 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (130) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X3, X6)) -> U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_ga(X1, X2)) 24.90/7.37 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> PJ_IN_GAAAG(X3, X2, X4, X5, X6) 24.90/7.37 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X2, X6)) -> U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_gg(X1, X2)) 24.90/7.37 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X3, X4, X5, X6) 24.90/7.37 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X2, X6)) -> U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_gg(X1, X2)) 24.90/7.37 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X4, X3, X5, X6) 24.90/7.37 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X4, X6)) -> U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_ga(X1, X2)) 24.90/7.37 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> PK_IN_GAAAG(X4, X2, X3, X5, X6) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.37 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.37 24.90/7.37 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.37 24.90/7.37 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 PK_IN_GAAAG(x1, x2, x3, x4, x5) = PK_IN_GAAAG(x1, x5) 24.90/7.37 24.90/7.37 U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7) 24.90/7.37 24.90/7.37 PJ_IN_GAAAG(x1, x2, x3, x4, x5) = PJ_IN_GAAAG(x1, x5) 24.90/7.37 24.90/7.37 U21_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U21_GAAAG(x1, x3, x6, x7) 24.90/7.37 24.90/7.37 U23_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U23_GAAAG(x1, x2, x6, x7) 24.90/7.37 24.90/7.37 U28_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U28_GAAAG(x1, x4, x6, x7) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (131) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (132) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X3, X6)) -> U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_ga(X1, X2)) 24.90/7.37 U21_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_ga(X1, X2)) -> PJ_IN_GAAAG(X3, X2, X4, X5, X6) 24.90/7.37 PJ_IN_GAAAG(X1, X2, .(X3, X4), X5, .(X2, X6)) -> U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_in_gg(X1, X2)) 24.90/7.37 U23_GAAAG(X1, X2, X3, X4, X5, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X3, X4, X5, X6) 24.90/7.37 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X2, X6)) -> U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_gg(X1, X2)) 24.90/7.37 U26_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X4, X3, X5, X6) 24.90/7.37 PK_IN_GAAAG(X1, X2, X3, .(X4, X5), .(X4, X6)) -> U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_in_ga(X1, X2)) 24.90/7.37 U28_GAAAG(X1, X2, X3, X4, X5, X6, lesscG_out_ga(X1, X2)) -> PK_IN_GAAAG(X4, X2, X3, X5, X6) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 PK_IN_GAAAG(x1, x2, x3, x4, x5) = PK_IN_GAAAG(x1, x5) 24.90/7.37 24.90/7.37 U26_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U26_GAAAG(x1, x2, x6, x7) 24.90/7.37 24.90/7.37 PJ_IN_GAAAG(x1, x2, x3, x4, x5) = PJ_IN_GAAAG(x1, x5) 24.90/7.37 24.90/7.37 U21_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U21_GAAAG(x1, x3, x6, x7) 24.90/7.37 24.90/7.37 U23_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U23_GAAAG(x1, x2, x6, x7) 24.90/7.37 24.90/7.37 U28_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U28_GAAAG(x1, x4, x6, x7) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (133) PiDPToQDPProof (SOUND) 24.90/7.37 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (134) 24.90/7.37 Obligation: 24.90/7.37 Q DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 PJ_IN_GAAAG(X1, .(X3, X6)) -> U21_GAAAG(X1, X3, X6, lesscF_in_ga(X1)) 24.90/7.37 U21_GAAAG(X1, X3, X6, lesscF_out_ga(X1)) -> PJ_IN_GAAAG(X3, X6) 24.90/7.37 PJ_IN_GAAAG(X1, .(X2, X6)) -> U23_GAAAG(X1, X2, X6, lesscF_in_gg(X1, X2)) 24.90/7.37 U23_GAAAG(X1, X2, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X6) 24.90/7.37 PK_IN_GAAAG(X1, .(X2, X6)) -> U26_GAAAG(X1, X2, X6, lesscG_in_gg(X1, X2)) 24.90/7.37 U26_GAAAG(X1, X2, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X6) 24.90/7.37 PK_IN_GAAAG(X1, .(X4, X6)) -> U28_GAAAG(X1, X4, X6, lesscG_in_ga(X1)) 24.90/7.37 U28_GAAAG(X1, X4, X6, lesscG_out_ga(X1)) -> PK_IN_GAAAG(X4, X6) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 lesscF_in_ga(0) -> lesscF_out_ga(0) 24.90/7.37 lesscF_in_ga(s(X1)) -> U81_ga(X1, lesscG_in_ga(X1)) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 lesscG_in_ga(0) -> lesscG_out_ga(0) 24.90/7.37 lesscG_in_ga(s(X1)) -> U79_ga(X1, lesscG_in_ga(X1)) 24.90/7.37 U81_ga(X1, lesscG_out_ga(X1)) -> lesscF_out_ga(s(X1)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 U79_ga(X1, lesscG_out_ga(X1)) -> lesscG_out_ga(s(X1)) 24.90/7.37 24.90/7.37 The set Q consists of the following terms: 24.90/7.37 24.90/7.37 lesscF_in_ga(x0) 24.90/7.37 lesscF_in_gg(x0, x1) 24.90/7.37 lesscG_in_gg(x0, x1) 24.90/7.37 lesscG_in_ga(x0) 24.90/7.37 U81_ga(x0, x1) 24.90/7.37 U81_gg(x0, x1, x2) 24.90/7.37 U79_gg(x0, x1, x2) 24.90/7.37 U79_ga(x0, x1) 24.90/7.37 24.90/7.37 We have to consider all (P,Q,R)-chains. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (135) QDPSizeChangeProof (EQUIVALENT) 24.90/7.37 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. 24.90/7.37 24.90/7.37 From the DPs we obtained the following set of size-change graphs: 24.90/7.37 *U21_GAAAG(X1, X3, X6, lesscF_out_ga(X1)) -> PJ_IN_GAAAG(X3, X6) 24.90/7.37 The graph contains the following edges 2 >= 1, 3 >= 2 24.90/7.37 24.90/7.37 24.90/7.37 *U26_GAAAG(X1, X2, X6, lesscG_out_gg(X1, X2)) -> PJ_IN_GAAAG(X2, X6) 24.90/7.37 The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2 24.90/7.37 24.90/7.37 24.90/7.37 *PJ_IN_GAAAG(X1, .(X3, X6)) -> U21_GAAAG(X1, X3, X6, lesscF_in_ga(X1)) 24.90/7.37 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3 24.90/7.37 24.90/7.37 24.90/7.37 *PJ_IN_GAAAG(X1, .(X2, X6)) -> U23_GAAAG(X1, X2, X6, lesscF_in_gg(X1, X2)) 24.90/7.37 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3 24.90/7.37 24.90/7.37 24.90/7.37 *U23_GAAAG(X1, X2, X6, lesscF_out_gg(X1, X2)) -> PK_IN_GAAAG(X2, X6) 24.90/7.37 The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2 24.90/7.37 24.90/7.37 24.90/7.37 *U28_GAAAG(X1, X4, X6, lesscG_out_ga(X1)) -> PK_IN_GAAAG(X4, X6) 24.90/7.37 The graph contains the following edges 2 >= 1, 3 >= 2 24.90/7.37 24.90/7.37 24.90/7.37 *PK_IN_GAAAG(X1, .(X2, X6)) -> U26_GAAAG(X1, X2, X6, lesscG_in_gg(X1, X2)) 24.90/7.37 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3 24.90/7.37 24.90/7.37 24.90/7.37 *PK_IN_GAAAG(X1, .(X4, X6)) -> U28_GAAAG(X1, X4, X6, lesscG_in_ga(X1)) 24.90/7.37 The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3 24.90/7.37 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (136) 24.90/7.37 YES 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (137) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 LESSG_IN_AA(s(X1), s(X2)) -> LESSG_IN_AA(X1, X2) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.37 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.37 24.90/7.37 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.37 24.90/7.37 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 LESSG_IN_AA(x1, x2) = LESSG_IN_AA 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (138) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (139) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 LESSG_IN_AA(s(X1), s(X2)) -> LESSG_IN_AA(X1, X2) 24.90/7.37 24.90/7.37 R is empty. 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 LESSG_IN_AA(x1, x2) = LESSG_IN_AA 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (140) PiDPToQDPProof (SOUND) 24.90/7.37 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (141) 24.90/7.37 Obligation: 24.90/7.37 Q DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 LESSG_IN_AA -> LESSG_IN_AA 24.90/7.37 24.90/7.37 R is empty. 24.90/7.37 Q is empty. 24.90/7.37 We have to consider all (P,Q,R)-chains. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (142) NonTerminationLoopProof (COMPLETE) 24.90/7.37 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 24.90/7.37 Found a loop by semiunifying a rule from P directly. 24.90/7.37 24.90/7.37 s = LESSG_IN_AA evaluates to t =LESSG_IN_AA 24.90/7.37 24.90/7.37 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 24.90/7.37 * Matcher: [ ] 24.90/7.37 * Semiunifier: [ ] 24.90/7.37 24.90/7.37 -------------------------------------------------------------------------------- 24.90/7.37 Rewriting sequence 24.90/7.37 24.90/7.37 The DP semiunifies directly so there is only one rewrite step from LESSG_IN_AA to LESSG_IN_AA. 24.90/7.37 24.90/7.37 24.90/7.37 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (143) 24.90/7.37 NO 24.90/7.37 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (144) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U12_AAA(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> MERGED_IN_AAA(X2, .(X3, X4), X5) 24.90/7.37 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U15_AAA(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> MERGED_IN_AAA(.(X1, X2), X4, X5) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.37 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.37 24.90/7.37 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.37 24.90/7.37 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 MERGED_IN_AAA(x1, x2, x3) = MERGED_IN_AAA 24.90/7.37 24.90/7.37 U12_AAA(x1, x2, x3, x4, x5, x6) = U12_AAA(x6) 24.90/7.37 24.90/7.37 U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (145) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (146) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X1, X5)) -> U12_AAA(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 U12_AAA(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> MERGED_IN_AAA(X2, .(X3, X4), X5) 24.90/7.37 MERGED_IN_AAA(.(X1, X2), .(X3, X4), .(X3, X5)) -> U15_AAA(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U15_AAA(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> MERGED_IN_AAA(.(X1, X2), X4, X5) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 MERGED_IN_AAA(x1, x2, x3) = MERGED_IN_AAA 24.90/7.37 24.90/7.37 U12_AAA(x1, x2, x3, x4, x5, x6) = U12_AAA(x6) 24.90/7.37 24.90/7.37 U15_AAA(x1, x2, x3, x4, x5, x6) = U15_AAA(x6) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (147) PiDPToQDPProof (SOUND) 24.90/7.37 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (148) 24.90/7.37 Obligation: 24.90/7.37 Q DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 MERGED_IN_AAA -> U12_AAA(lesscF_in_aa) 24.90/7.37 U12_AAA(lesscF_out_aa(X1)) -> MERGED_IN_AAA 24.90/7.37 MERGED_IN_AAA -> U15_AAA(lesscG_in_aa) 24.90/7.37 U15_AAA(lesscG_out_aa(X3)) -> MERGED_IN_AAA 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 lesscF_in_aa -> lesscF_out_aa(0) 24.90/7.37 lesscF_in_aa -> U81_aa(lesscG_in_aa) 24.90/7.37 lesscG_in_aa -> lesscG_out_aa(0) 24.90/7.37 lesscG_in_aa -> U79_aa(lesscG_in_aa) 24.90/7.37 U81_aa(lesscG_out_aa(X1)) -> lesscF_out_aa(s(X1)) 24.90/7.37 U79_aa(lesscG_out_aa(X1)) -> lesscG_out_aa(s(X1)) 24.90/7.37 24.90/7.37 The set Q consists of the following terms: 24.90/7.37 24.90/7.37 lesscF_in_aa 24.90/7.37 lesscG_in_aa 24.90/7.37 U81_aa(x0) 24.90/7.37 U79_aa(x0) 24.90/7.37 24.90/7.37 We have to consider all (P,Q,R)-chains. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (149) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.37 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.37 24.90/7.37 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.37 24.90/7.37 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 SPLITA_IN_AAA(x1, x2, x3) = SPLITA_IN_AAA 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (150) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (151) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 SPLITA_IN_AAA(.(X1, X2), .(X1, X3), X4) -> SPLITA_IN_AAA(X2, X4, X3) 24.90/7.37 24.90/7.37 R is empty. 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 SPLITA_IN_AAA(x1, x2, x3) = SPLITA_IN_AAA 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (152) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> MSE_IN_AA(X4, X6) 24.90/7.37 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.37 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> MSE_IN_AA(X5, X7) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 mscH_in_aaa(X1, [], .(X1, [])) -> mscH_out_aaa(X1, [], .(X1, [])) 24.90/7.37 mscH_in_aaa(X1, .(X2, X3), X4) -> U80_aaa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U80_aaa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscH_out_aaa(X1, .(X2, X3), X4) 24.90/7.37 lesscG_in_gg(0, s(X1)) -> lesscG_out_gg(0, s(X1)) 24.90/7.37 lesscG_in_gg(s(X1), s(X2)) -> U79_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U79_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscG_out_gg(s(X1), s(X2)) 24.90/7.37 lesscF_in_ga(0, X1) -> lesscF_out_ga(0, X1) 24.90/7.37 lesscF_in_ga(s(X1), X2) -> U81_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 lesscG_in_ga(0, s(X1)) -> lesscG_out_ga(0, s(X1)) 24.90/7.37 lesscG_in_ga(s(X1), s(X2)) -> U79_ga(X1, X2, lesscG_in_ga(X1, X2)) 24.90/7.37 U79_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscG_out_ga(s(X1), s(X2)) 24.90/7.37 U81_ga(X1, X2, lesscG_out_ga(X1, X2)) -> lesscF_out_ga(s(X1), X2) 24.90/7.37 lesscF_in_gg(0, X1) -> lesscF_out_gg(0, X1) 24.90/7.37 lesscF_in_gg(s(X1), X2) -> U81_gg(X1, X2, lesscG_in_gg(X1, X2)) 24.90/7.37 U81_gg(X1, X2, lesscG_out_gg(X1, X2)) -> lesscF_out_gg(s(X1), X2) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 mscH_in_aaa(x1, x2, x3) = mscH_in_aaa 24.90/7.37 24.90/7.37 mscH_out_aaa(x1, x2, x3) = mscH_out_aaa 24.90/7.37 24.90/7.37 U80_aaa(x1, x2, x3, x4, x5) = U80_aaa(x5) 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 lesscG_in_gg(x1, x2) = lesscG_in_gg(x1, x2) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 lesscG_out_gg(x1, x2) = lesscG_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U79_gg(x1, x2, x3) = U79_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 lesscF_in_ga(x1, x2) = lesscF_in_ga(x1) 24.90/7.37 24.90/7.37 lesscF_out_ga(x1, x2) = lesscF_out_ga(x1) 24.90/7.37 24.90/7.37 U81_ga(x1, x2, x3) = U81_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscG_in_ga(x1, x2) = lesscG_in_ga(x1) 24.90/7.37 24.90/7.37 lesscG_out_ga(x1, x2) = lesscG_out_ga(x1) 24.90/7.37 24.90/7.37 U79_ga(x1, x2, x3) = U79_ga(x1, x3) 24.90/7.37 24.90/7.37 lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2) 24.90/7.37 24.90/7.37 lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2) 24.90/7.37 24.90/7.37 U81_gg(x1, x2, x3) = U81_gg(x1, x2, x3) 24.90/7.37 24.90/7.37 PC_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = PC_IN_AAAAAAAA 24.90/7.37 24.90/7.37 U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9) 24.90/7.37 24.90/7.37 MSE_IN_AA(x1, x2) = MSE_IN_AA 24.90/7.37 24.90/7.37 U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (153) UsableRulesProof (EQUIVALENT) 24.90/7.37 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (154) 24.90/7.37 Obligation: 24.90/7.37 Pi DP problem: 24.90/7.37 The TRS P consists of the following rules: 24.90/7.37 24.90/7.37 PC_IN_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8) -> U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> MSE_IN_AA(X4, X6) 24.90/7.37 MSE_IN_AA(.(X1, .(X2, X3)), X4) -> PC_IN_AAAAAAAA(X1, X2, X3, X5, X6, X7, X8, X4) 24.90/7.37 U4_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U6_AAAAAAAA(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> MSE_IN_AA(X5, X7) 24.90/7.37 24.90/7.37 The TRS R consists of the following rules: 24.90/7.37 24.90/7.37 splitcB_in_aaaa(X1, X2, .(X1, X3), X4) -> U69_aaaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 mscE_in_aa([], []) -> mscE_out_aa([], []) 24.90/7.37 mscE_in_aa(.(X1, []), .(X1, [])) -> mscE_out_aa(.(X1, []), .(X1, [])) 24.90/7.37 mscE_in_aa(.(X1, .(X2, X3)), X4) -> U74_aa(X1, X2, X3, X4, qcC_in_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) 24.90/7.37 U69_aaaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcB_out_aaaa(X1, X2, .(X1, X3), X4) 24.90/7.37 U74_aa(X1, X2, X3, X4, qcC_out_aaaaaaaa(X1, X2, X3, X5, X6, X7, X8, X4)) -> mscE_out_aa(.(X1, .(X2, X3)), X4) 24.90/7.37 splitcA_in_aaa([], [], []) -> splitcA_out_aaa([], [], []) 24.90/7.37 splitcA_in_aaa(.(X1, X2), .(X1, X3), X4) -> U68_aaa(X1, X2, X3, X4, splitcA_in_aaa(X2, X4, X3)) 24.90/7.37 qcC_in_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) -> U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_in_aaaa(X1, .(X2, X3), X4, X5)) 24.90/7.37 U68_aaa(X1, X2, X3, X4, splitcA_out_aaa(X2, X4, X3)) -> splitcA_out_aaa(.(X1, X2), .(X1, X3), X4) 24.90/7.37 U70_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, splitcB_out_aaaa(X1, .(X2, X3), X4, X5)) -> U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X4, X6)) 24.90/7.37 U71_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X4, X6)) -> U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_in_aa(X5, X7)) 24.90/7.37 U72_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mscE_out_aa(X5, X7)) -> U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_in_aaa(X6, X7, X8)) 24.90/7.37 U73_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8, mergecD_out_aaa(X6, X7, X8)) -> qcC_out_aaaaaaaa(X1, X2, X3, X4, X5, X6, X7, X8) 24.90/7.37 mergecD_in_aaa([], X1, X1) -> mergecD_out_aaa([], X1, X1) 24.90/7.37 mergecD_in_aaa(X1, [], X1) -> mergecD_out_aaa(X1, [], X1) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) -> U75_aaa(X1, X2, X3, X4, X5, lesscF_in_aa(X1, X3)) 24.90/7.37 mergecD_in_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) -> U77_aaa(X1, X2, X3, X4, X5, lesscG_in_aa(X3, X1)) 24.90/7.37 U75_aaa(X1, X2, X3, X4, X5, lesscF_out_aa(X1, X3)) -> U76_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(X2, .(X3, X4), X5)) 24.90/7.37 U77_aaa(X1, X2, X3, X4, X5, lesscG_out_aa(X3, X1)) -> U78_aaa(X1, X2, X3, X4, X5, mergecD_in_aaa(.(X1, X2), X4, X5)) 24.90/7.37 lesscF_in_aa(0, X1) -> lesscF_out_aa(0, X1) 24.90/7.37 lesscF_in_aa(s(X1), X2) -> U81_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U76_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(X2, .(X3, X4), X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X1, X5)) 24.90/7.37 lesscG_in_aa(0, s(X1)) -> lesscG_out_aa(0, s(X1)) 24.90/7.37 lesscG_in_aa(s(X1), s(X2)) -> U79_aa(X1, X2, lesscG_in_aa(X1, X2)) 24.90/7.37 U78_aaa(X1, X2, X3, X4, X5, mergecD_out_aaa(.(X1, X2), X4, X5)) -> mergecD_out_aaa(.(X1, X2), .(X3, X4), .(X3, X5)) 24.90/7.37 U81_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscF_out_aa(s(X1), X2) 24.90/7.37 U79_aa(X1, X2, lesscG_out_aa(X1, X2)) -> lesscG_out_aa(s(X1), s(X2)) 24.90/7.37 24.90/7.37 The argument filtering Pi contains the following mapping: 24.90/7.37 [] = [] 24.90/7.37 24.90/7.37 splitcB_in_aaaa(x1, x2, x3, x4) = splitcB_in_aaaa 24.90/7.37 24.90/7.37 U69_aaaa(x1, x2, x3, x4, x5) = U69_aaaa(x5) 24.90/7.37 24.90/7.37 splitcA_in_aaa(x1, x2, x3) = splitcA_in_aaa 24.90/7.37 24.90/7.37 splitcA_out_aaa(x1, x2, x3) = splitcA_out_aaa 24.90/7.37 24.90/7.37 U68_aaa(x1, x2, x3, x4, x5) = U68_aaa(x5) 24.90/7.37 24.90/7.37 splitcB_out_aaaa(x1, x2, x3, x4) = splitcB_out_aaaa 24.90/7.37 24.90/7.37 mscE_in_aa(x1, x2) = mscE_in_aa 24.90/7.37 24.90/7.37 mscE_out_aa(x1, x2) = mscE_out_aa 24.90/7.37 24.90/7.37 U74_aa(x1, x2, x3, x4, x5) = U74_aa(x5) 24.90/7.37 24.90/7.37 qcC_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_in_aaaaaaaa 24.90/7.37 24.90/7.37 U70_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U71_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U72_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 U73_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_aaaaaaaa(x9) 24.90/7.37 24.90/7.37 mergecD_in_aaa(x1, x2, x3) = mergecD_in_aaa 24.90/7.37 24.90/7.37 mergecD_out_aaa(x1, x2, x3) = mergecD_out_aaa 24.90/7.37 24.90/7.37 U75_aaa(x1, x2, x3, x4, x5, x6) = U75_aaa(x6) 24.90/7.37 24.90/7.37 lesscF_in_aa(x1, x2) = lesscF_in_aa 24.90/7.37 24.90/7.37 lesscF_out_aa(x1, x2) = lesscF_out_aa(x1) 24.90/7.37 24.90/7.37 U81_aa(x1, x2, x3) = U81_aa(x3) 24.90/7.37 24.90/7.37 lesscG_in_aa(x1, x2) = lesscG_in_aa 24.90/7.37 24.90/7.37 lesscG_out_aa(x1, x2) = lesscG_out_aa(x1) 24.90/7.37 24.90/7.37 U79_aa(x1, x2, x3) = U79_aa(x3) 24.90/7.37 24.90/7.37 U76_aaa(x1, x2, x3, x4, x5, x6) = U76_aaa(x6) 24.90/7.37 24.90/7.37 U77_aaa(x1, x2, x3, x4, x5, x6) = U77_aaa(x6) 24.90/7.37 24.90/7.37 U78_aaa(x1, x2, x3, x4, x5, x6) = U78_aaa(x6) 24.90/7.37 24.90/7.37 qcC_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8) = qcC_out_aaaaaaaa 24.90/7.37 24.90/7.37 .(x1, x2) = .(x1, x2) 24.90/7.37 24.90/7.37 s(x1) = s(x1) 24.90/7.37 24.90/7.37 0 = 0 24.90/7.37 24.90/7.37 PC_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8) = PC_IN_AAAAAAAA 24.90/7.37 24.90/7.37 U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U4_AAAAAAAA(x9) 24.90/7.37 24.90/7.37 MSE_IN_AA(x1, x2) = MSE_IN_AA 24.90/7.37 24.90/7.37 U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U6_AAAAAAAA(x9) 24.90/7.37 24.90/7.37 24.90/7.37 We have to consider all (P,R,Pi)-chains 24.90/7.37 ---------------------------------------- 24.90/7.37 24.90/7.37 (155) PrologToIRSwTTransformerProof (SOUND) 24.90/7.37 Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert 24.90/7.37 24.90/7.37 { 24.90/7.37 "root": 25, 24.90/7.37 "program": { 24.90/7.37 "directives": [], 24.90/7.37 "clauses": [ 24.90/7.37 [ 24.90/7.37 "(ms ([]) ([]))", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(ms (. X ([])) (. X ([])))", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(ms (. X (. Y Xs)) Ys)", 24.90/7.37 "(',' (split (. X (. Y Xs)) X1s X2s) (',' (ms X1s Y1s) (',' (ms X2s Y2s) (merge Y1s Y2s Ys))))" 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(split ([]) ([]) ([]))", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(split (. X Xs) (. X Ys) Zs)", 24.90/7.37 "(split Xs Zs Ys)" 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(merge ([]) Xs Xs)", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(merge Xs ([]) Xs)", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(merge (. X Xs) (. Y Ys) (. X Zs))", 24.90/7.37 "(',' (less X (s Y)) (merge Xs (. Y Ys) Zs))" 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(merge (. X Xs) (. Y Ys) (. Y Zs))", 24.90/7.37 "(',' (less Y X) (merge (. X Xs) Ys Zs))" 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(less (0) (s X1))", 24.90/7.37 null 24.90/7.37 ], 24.90/7.37 [ 24.90/7.37 "(less (s X) (s Y))", 24.90/7.37 "(less X Y)" 24.90/7.37 ] 24.90/7.37 ] 24.90/7.37 }, 24.90/7.37 "graph": { 24.90/7.37 "nodes": { 24.90/7.37 "type": "Nodes", 24.90/7.37 "594": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(split T45 X62 X61)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": [ 24.90/7.37 "X61", 24.90/7.37 "X62" 24.90/7.37 ], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "751": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(ms T75 X107)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": ["X107"], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "872": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(ms T54 X26)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": ["X26"], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "477": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(true)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": [], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "752": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(merge T77 T76 X108)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": ["X108"], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "873": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": -1, 24.90/7.37 "scope": -1, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": ["T19"], 24.90/7.37 "free": [], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "478": { 24.90/7.37 "goal": [], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": [], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "599": { 24.90/7.37 "goal": [ 24.90/7.37 { 24.90/7.37 "clause": 3, 24.90/7.37 "scope": 4, 24.90/7.37 "term": "(split T45 X62 X61)" 24.90/7.37 }, 24.90/7.37 { 24.90/7.37 "clause": 4, 24.90/7.37 "scope": 4, 24.90/7.37 "term": "(split T45 X62 X61)" 24.90/7.37 } 24.90/7.37 ], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": [], 24.90/7.37 "free": [ 24.90/7.37 "X61", 24.90/7.37 "X62" 24.90/7.37 ], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "874": { 24.90/7.37 "goal": [ 24.90/7.37 { 24.90/7.37 "clause": 5, 24.90/7.37 "scope": 9, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 }, 24.90/7.37 { 24.90/7.37 "clause": 6, 24.90/7.37 "scope": 9, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 }, 24.90/7.37 { 24.90/7.37 "clause": 7, 24.90/7.37 "scope": 9, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 }, 24.90/7.37 { 24.90/7.37 "clause": 8, 24.90/7.37 "scope": 9, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 } 24.90/7.37 ], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": { 24.90/7.37 "type": "PlainIntegerRelationState", 24.90/7.37 "relations": [] 24.90/7.37 }, 24.90/7.37 "ground": ["T19"], 24.90/7.37 "free": [], 24.90/7.37 "exprvars": [] 24.90/7.37 } 24.90/7.37 }, 24.90/7.37 "875": { 24.90/7.37 "goal": [{ 24.90/7.37 "clause": 5, 24.90/7.37 "scope": 9, 24.90/7.37 "term": "(merge T179 T178 T19)" 24.90/7.37 }], 24.90/7.37 "kb": { 24.90/7.37 "nonunifying": [], 24.90/7.37 "intvars": {}, 24.90/7.37 "arithmetic": 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"goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "977": { 25.06/7.38 "goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "616": { 25.06/7.38 "goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "464": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": 1, 25.06/7.38 "scope": 1, 25.06/7.38 "term": "(ms T1 T2)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": ["T2"], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "860": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(',' (less T167 T168) (merge (. T168 T170) T169 X200))" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": ["X200"], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "465": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": 2, 25.06/7.38 "scope": 1, 25.06/7.38 "term": "(ms T1 T2)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": ["T2"], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "740": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(',' (split (. T69 (. T70 T71)) X104 X105) (',' (ms X104 X106) (',' (ms X105 X107) (merge X106 X107 X108))))" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [ 25.06/7.38 "X108", 25.06/7.38 "X104", 25.06/7.38 "X105", 25.06/7.38 "X106", 25.06/7.38 "X107" 25.06/7.38 ], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "861": { 25.06/7.38 "goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "741": { 25.06/7.38 "goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "742": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(split (. T69 (. T70 T71)) X104 X105)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [ 25.06/7.38 "X104", 25.06/7.38 "X105" 25.06/7.38 ], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "743": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(',' (ms T72 X106) (',' (ms T73 X107) (merge X106 X107 X108)))" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [ 25.06/7.38 "X108", 25.06/7.38 "X106", 25.06/7.38 "X107" 25.06/7.38 ], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "865": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(less T167 T168)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "866": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(merge (. T173 T174) T175 X200)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": ["X200"], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "504": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(',' (split (. T20 (. T21 T22)) X23 X24) (',' (ms X23 X25) (',' (ms X24 X26) (merge X25 X26 T19))))" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": ["T19"], 25.06/7.38 "free": [ 25.06/7.38 "X23", 25.06/7.38 "X24", 25.06/7.38 "X25", 25.06/7.38 "X26" 25.06/7.38 ], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "747": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(ms T72 X106)" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": ["X106"], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "748": { 25.06/7.38 "goal": [{ 25.06/7.38 "clause": -1, 25.06/7.38 "scope": -1, 25.06/7.38 "term": "(',' (ms T75 X107) (merge T74 X107 X108))" 25.06/7.38 }], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [ 25.06/7.38 "X108", 25.06/7.38 "X107" 25.06/7.38 ], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "507": { 25.06/7.38 "goal": [], 25.06/7.38 "kb": { 25.06/7.38 "nonunifying": [], 25.06/7.38 "intvars": {}, 25.06/7.38 "arithmetic": { 25.06/7.38 "type": "PlainIntegerRelationState", 25.06/7.38 "relations": [] 25.06/7.38 }, 25.06/7.38 "ground": [], 25.06/7.38 "free": [], 25.06/7.38 "exprvars": [] 25.06/7.38 } 25.06/7.38 } 25.06/7.38 }, 25.06/7.38 "edges": [ 25.06/7.38 { 25.06/7.38 "from": 25, 25.06/7.38 "to": 26, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 26, 25.06/7.38 "to": 27, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 26, 25.06/7.38 "to": 28, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 27, 25.06/7.38 "to": 450, 25.06/7.38 "label": "EVAL with clause\nms([], []).\nand substitutionT1 -> [],\nT2 -> []" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 27, 25.06/7.38 "to": 453, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 28, 25.06/7.38 "to": 464, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 28, 25.06/7.38 "to": 465, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 450, 25.06/7.38 "to": 457, 25.06/7.38 "label": "SUCCESS" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 464, 25.06/7.38 "to": 477, 25.06/7.38 "label": "EVAL with clause\nms(.(X6, []), .(X6, [])).\nand substitutionX6 -> T7,\nT1 -> .(T7, []),\nT2 -> .(T7, [])" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 464, 25.06/7.38 "to": 478, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 465, 25.06/7.38 "to": 504, 25.06/7.38 "label": "EVAL with clause\nms(.(X19, .(X20, X21)), X22) :- ','(split(.(X19, .(X20, X21)), X23, X24), ','(ms(X23, X25), ','(ms(X24, X26), merge(X25, X26, X22)))).\nand substitutionX19 -> T20,\nX20 -> T21,\nX21 -> T22,\nT1 -> .(T20, .(T21, T22)),\nT2 -> T19,\nX22 -> T19,\nT16 -> T20,\nT17 -> T21,\nT18 -> T22" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 465, 25.06/7.38 "to": 507, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 477, 25.06/7.38 "to": 480, 25.06/7.38 "label": "SUCCESS" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 504, 25.06/7.38 "to": 549, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 504, 25.06/7.38 "to": 550, 25.06/7.38 "label": "SPLIT 2\nreplacements:X23 -> T23,\nX24 -> T24" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 549, 25.06/7.38 "to": 551, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 550, 25.06/7.38 "to": 713, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 550, 25.06/7.38 "to": 714, 25.06/7.38 "label": "SPLIT 2\nreplacements:X25 -> T53,\nT24 -> T54" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 551, 25.06/7.38 "to": 552, 25.06/7.38 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 552, 25.06/7.38 "to": 559, 25.06/7.38 "label": "ONLY EVAL with clause\nsplit(.(X39, X40), .(X39, X41), X42) :- split(X40, X42, X41).\nand substitutionT20 -> T33,\nX39 -> T33,\nT21 -> T36,\nT22 -> T37,\nX40 -> .(T36, T37),\nX41 -> X43,\nX23 -> .(T33, X43),\nX24 -> X44,\nX42 -> X44,\nT34 -> T36,\nT35 -> T37" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 559, 25.06/7.38 "to": 565, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 565, 25.06/7.38 "to": 566, 25.06/7.38 "label": "BACKTRACK\nfor clause: split([], [], [])because of non-unification" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 566, 25.06/7.38 "to": 594, 25.06/7.38 "label": "ONLY EVAL with clause\nsplit(.(X57, X58), .(X57, X59), X60) :- split(X58, X60, X59).\nand substitutionT36 -> T43,\nX57 -> T43,\nT37 -> T45,\nX58 -> T45,\nX59 -> X61,\nX44 -> .(T43, X61),\nX43 -> X62,\nX60 -> X62,\nT44 -> T45" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 594, 25.06/7.38 "to": 599, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 599, 25.06/7.38 "to": 603, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 599, 25.06/7.38 "to": 605, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 603, 25.06/7.38 "to": 611, 25.06/7.38 "label": "EVAL with clause\nsplit([], [], []).\nand substitutionT45 -> [],\nX62 -> [],\nX61 -> []" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 603, 25.06/7.38 "to": 614, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 605, 25.06/7.38 "to": 639, 25.06/7.38 "label": "EVAL with clause\nsplit(.(X75, X76), .(X75, X77), X78) :- split(X76, X78, X77).\nand substitutionX75 -> T50,\nX76 -> T52,\nT45 -> .(T50, T52),\nX77 -> X79,\nX62 -> .(T50, X79),\nX61 -> X80,\nX78 -> X80,\nT51 -> T52" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 605, 25.06/7.38 "to": 643, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 611, 25.06/7.38 "to": 616, 25.06/7.38 "label": "SUCCESS" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 639, 25.06/7.38 "to": 594, 25.06/7.38 "label": "INSTANCE with matching:\nT45 -> T52\nX62 -> X80\nX61 -> X79" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 713, 25.06/7.38 "to": 716, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 714, 25.06/7.38 "to": 872, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 714, 25.06/7.38 "to": 873, 25.06/7.38 "label": "SPLIT 2\nreplacements:X26 -> T178,\nT53 -> T179" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 716, 25.06/7.38 "to": 717, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 716, 25.06/7.38 "to": 718, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 717, 25.06/7.38 "to": 719, 25.06/7.38 "label": "EVAL with clause\nms([], []).\nand substitutionT23 -> [],\nX25 -> []" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 717, 25.06/7.38 "to": 720, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 718, 25.06/7.38 "to": 722, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 718, 25.06/7.38 "to": 723, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 719, 25.06/7.38 "to": 721, 25.06/7.38 "label": "SUCCESS" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 722, 25.06/7.38 "to": 724, 25.06/7.38 "label": "EVAL with clause\nms(.(X85, []), .(X85, [])).\nand substitutionX85 -> T59,\nT23 -> .(T59, []),\nX25 -> .(T59, [])" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 722, 25.06/7.38 "to": 725, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 723, 25.06/7.38 "to": 740, 25.06/7.38 "label": "EVAL with clause\nms(.(X100, .(X101, X102)), X103) :- ','(split(.(X100, .(X101, X102)), X104, X105), ','(ms(X104, X106), ','(ms(X105, X107), merge(X106, X107, X103)))).\nand substitutionX100 -> T69,\nX101 -> T70,\nX102 -> T71,\nT23 -> .(T69, .(T70, T71)),\nX25 -> X108,\nX103 -> X108,\nT66 -> T69,\nT67 -> T70,\nT68 -> T71" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 723, 25.06/7.38 "to": 741, 25.06/7.38 "label": "EVAL-BACKTRACK" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 724, 25.06/7.38 "to": 726, 25.06/7.38 "label": "SUCCESS" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 740, 25.06/7.38 "to": 742, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 740, 25.06/7.38 "to": 743, 25.06/7.38 "label": "SPLIT 2\nreplacements:X104 -> T72,\nX105 -> T73" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 742, 25.06/7.38 "to": 549, 25.06/7.38 "label": "INSTANCE with matching:\nT20 -> T69\nT21 -> T70\nT22 -> T71\nX23 -> X104\nX24 -> X105" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 743, 25.06/7.38 "to": 747, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 743, 25.06/7.38 "to": 748, 25.06/7.38 "label": "SPLIT 2\nreplacements:X106 -> T74,\nT73 -> T75" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 747, 25.06/7.38 "to": 713, 25.06/7.38 "label": "INSTANCE with matching:\nT23 -> T72\nX25 -> X106" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 748, 25.06/7.38 "to": 751, 25.06/7.38 "label": "SPLIT 1" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 748, 25.06/7.38 "to": 752, 25.06/7.38 "label": "SPLIT 2\nreplacements:X107 -> T76,\nT74 -> T77" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 751, 25.06/7.38 "to": 713, 25.06/7.38 "label": "INSTANCE with matching:\nT23 -> T75\nX25 -> X107" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 752, 25.06/7.38 "to": 756, 25.06/7.38 "label": "CASE" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 756, 25.06/7.38 "to": 759, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 756, 25.06/7.38 "to": 760, 25.06/7.38 "label": "PARALLEL" 25.06/7.38 }, 25.06/7.38 { 25.06/7.38 "from": 759, 25.06/7.39 "to": 764, 25.06/7.39 "label": "EVAL with clause\nmerge([], X115, X115).\nand substitutionT77 -> [],\nT76 -> T84,\nX115 -> T84,\nX108 -> T84" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 759, 25.06/7.39 "to": 767, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 760, 25.06/7.39 "to": 769, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 760, 25.06/7.39 "to": 770, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 764, 25.06/7.39 "to": 768, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 769, 25.06/7.39 "to": 774, 25.06/7.39 "label": "EVAL with clause\nmerge(X120, [], X120).\nand substitutionT77 -> T89,\nX120 -> T89,\nT76 -> [],\nX108 -> T89" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 769, 25.06/7.39 "to": 775, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 770, 25.06/7.39 "to": 778, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 770, 25.06/7.39 "to": 780, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 774, 25.06/7.39 "to": 776, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 778, 25.06/7.39 "to": 787, 25.06/7.39 "label": "EVAL with clause\nmerge(.(X145, X146), .(X147, X148), .(X145, X149)) :- ','(less(X145, s(X147)), merge(X146, .(X147, X148), X149)).\nand substitutionX145 -> T110,\nX146 -> T112,\nT77 -> .(T110, T112),\nX147 -> T111,\nX148 -> T113,\nT76 -> .(T111, T113),\nX149 -> X150,\nX108 -> .(T110, X150),\nT106 -> T110,\nT108 -> T111,\nT107 -> T112,\nT109 -> T113" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 778, 25.06/7.39 "to": 789, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 780, 25.06/7.39 "to": 860, 25.06/7.39 "label": "EVAL with clause\nmerge(.(X195, X196), .(X197, X198), .(X197, X199)) :- ','(less(X197, X195), merge(.(X195, X196), X198, X199)).\nand substitutionX195 -> T168,\nX196 -> T170,\nT77 -> .(T168, T170),\nX197 -> T167,\nX198 -> T169,\nT76 -> .(T167, T169),\nX199 -> X200,\nX108 -> .(T167, X200),\nT165 -> T167,\nT163 -> T168,\nT166 -> T169,\nT164 -> T170" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 780, 25.06/7.39 "to": 861, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 787, 25.06/7.39 "to": 798, 25.06/7.39 "label": "SPLIT 1" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 787, 25.06/7.39 "to": 799, 25.06/7.39 "label": "SPLIT 2\nnew knowledge:\nT110 is ground\nreplacements:T112 -> T116,\nT111 -> T117,\nT113 -> T118" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 798, 25.06/7.39 "to": 800, 25.06/7.39 "label": "CASE" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 799, 25.06/7.39 "to": 752, 25.06/7.39 "label": "INSTANCE with matching:\nT77 -> T116\nT76 -> .(T117, T118)\nX108 -> X150" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 800, 25.06/7.39 "to": 803, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 800, 25.06/7.39 "to": 804, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 803, 25.06/7.39 "to": 812, 25.06/7.39 "label": "EVAL with clause\nless(0, s(X159)).\nand substitutionT110 -> 0,\nT111 -> T125,\nX159 -> T125" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 803, 25.06/7.39 "to": 813, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 804, 25.06/7.39 "to": 820, 25.06/7.39 "label": "EVAL with clause\nless(s(X164), s(X165)) :- less(X164, X165).\nand substitutionX164 -> T132,\nT110 -> s(T132),\nT111 -> T133,\nX165 -> T133,\nT130 -> T132,\nT131 -> T133" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 804, 25.06/7.39 "to": 823, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 812, 25.06/7.39 "to": 814, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 820, 25.06/7.39 "to": 831, 25.06/7.39 "label": "CASE" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 831, 25.06/7.39 "to": 834, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 831, 25.06/7.39 "to": 835, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 834, 25.06/7.39 "to": 840, 25.06/7.39 "label": "EVAL with clause\nless(0, s(X172)).\nand substitutionT132 -> 0,\nX172 -> T140,\nT133 -> s(T140)" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 834, 25.06/7.39 "to": 842, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 835, 25.06/7.39 "to": 846, 25.06/7.39 "label": "EVAL with clause\nless(s(X177), s(X178)) :- less(X177, X178).\nand substitutionX177 -> T147,\nT132 -> s(T147),\nX178 -> T148,\nT133 -> s(T148),\nT145 -> T147,\nT146 -> T148" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 835, 25.06/7.39 "to": 847, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 840, 25.06/7.39 "to": 844, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 846, 25.06/7.39 "to": 820, 25.06/7.39 "label": "INSTANCE with matching:\nT132 -> T147\nT133 -> T148" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 860, 25.06/7.39 "to": 865, 25.06/7.39 "label": "SPLIT 1" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 860, 25.06/7.39 "to": 866, 25.06/7.39 "label": "SPLIT 2\nnew knowledge:\nT167 is ground\nreplacements:T168 -> T173,\nT170 -> T174,\nT169 -> T175" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 865, 25.06/7.39 "to": 820, 25.06/7.39 "label": "INSTANCE with matching:\nT132 -> T167\nT133 -> T168" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 866, 25.06/7.39 "to": 752, 25.06/7.39 "label": "INSTANCE with matching:\nT77 -> .(T173, T174)\nT76 -> T175\nX108 -> X200" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 872, 25.06/7.39 "to": 713, 25.06/7.39 "label": "INSTANCE with matching:\nT23 -> T54\nX25 -> X26" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 873, 25.06/7.39 "to": 874, 25.06/7.39 "label": "CASE" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 874, 25.06/7.39 "to": 875, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 874, 25.06/7.39 "to": 876, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 875, 25.06/7.39 "to": 881, 25.06/7.39 "label": "EVAL with clause\nmerge([], X213, X213).\nand substitutionT179 -> [],\nT178 -> T186,\nX213 -> T186,\nT19 -> T186" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 875, 25.06/7.39 "to": 882, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 876, 25.06/7.39 "to": 884, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 876, 25.06/7.39 "to": 885, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 881, 25.06/7.39 "to": 883, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 884, 25.06/7.39 "to": 886, 25.06/7.39 "label": "EVAL with clause\nmerge(X218, [], X218).\nand substitutionT179 -> T191,\nX218 -> T191,\nT178 -> [],\nT19 -> T191" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 884, 25.06/7.39 "to": 887, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 885, 25.06/7.39 "to": 1072, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 885, 25.06/7.39 "to": 1073, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 886, 25.06/7.39 "to": 977, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1072, 25.06/7.39 "to": 1074, 25.06/7.39 "label": "EVAL with clause\nmerge(.(X239, X240), .(X241, X242), .(X239, X243)) :- ','(less(X239, s(X241)), merge(X240, .(X241, X242), X243)).\nand substitutionX239 -> T212,\nX240 -> T218,\nT179 -> .(T212, T218),\nX241 -> T217,\nX242 -> T219,\nT178 -> .(T217, T219),\nX243 -> T216,\nT19 -> .(T212, T216),\nT214 -> T217,\nT213 -> T218,\nT215 -> T219" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1072, 25.06/7.39 "to": 1075, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1073, 25.06/7.39 "to": 1094, 25.06/7.39 "label": "EVAL with clause\nmerge(.(X286, X287), .(X288, X289), .(X288, X290)) :- ','(less(X288, X286), merge(.(X286, X287), X289, X290)).\nand substitutionX286 -> T274,\nX287 -> T276,\nT179 -> .(T274, T276),\nX288 -> T271,\nX289 -> T275,\nT178 -> .(T271, T275),\nX290 -> T273,\nT19 -> .(T271, T273),\nT269 -> T274,\nT272 -> T275,\nT270 -> T276" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1073, 25.06/7.39 "to": 1095, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1074, 25.06/7.39 "to": 1076, 25.06/7.39 "label": "SPLIT 1" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1074, 25.06/7.39 "to": 1077, 25.06/7.39 "label": "SPLIT 2\nnew knowledge:\nT212 is ground\nreplacements:T218 -> T222,\nT217 -> T223,\nT219 -> T224" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1076, 25.06/7.39 "to": 1078, 25.06/7.39 "label": "CASE" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1077, 25.06/7.39 "to": 873, 25.06/7.39 "label": "INSTANCE with matching:\nT179 -> T222\nT178 -> .(T223, T224)\nT19 -> T216" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1078, 25.06/7.39 "to": 1079, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1078, 25.06/7.39 "to": 1080, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1079, 25.06/7.39 "to": 1081, 25.06/7.39 "label": "EVAL with clause\nless(0, s(X252)).\nand substitutionT212 -> 0,\nT217 -> T231,\nX252 -> T231" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1079, 25.06/7.39 "to": 1082, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1080, 25.06/7.39 "to": 1084, 25.06/7.39 "label": "EVAL with clause\nless(s(X257), s(X258)) :- less(X257, X258).\nand substitutionX257 -> T236,\nT212 -> s(T236),\nT217 -> T238,\nX258 -> T238,\nT237 -> T238" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1080, 25.06/7.39 "to": 1085, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1081, 25.06/7.39 "to": 1083, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1084, 25.06/7.39 "to": 1086, 25.06/7.39 "label": "CASE" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1086, 25.06/7.39 "to": 1087, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1086, 25.06/7.39 "to": 1088, 25.06/7.39 "label": "PARALLEL" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1087, 25.06/7.39 "to": 1089, 25.06/7.39 "label": "EVAL with clause\nless(0, s(X265)).\nand substitutionT236 -> 0,\nX265 -> T245,\nT238 -> s(T245)" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1087, 25.06/7.39 "to": 1090, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1088, 25.06/7.39 "to": 1092, 25.06/7.39 "label": "EVAL with clause\nless(s(X270), s(X271)) :- less(X270, X271).\nand substitutionX270 -> T250,\nT236 -> s(T250),\nX271 -> T252,\nT238 -> s(T252),\nT251 -> T252" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1088, 25.06/7.39 "to": 1093, 25.06/7.39 "label": "EVAL-BACKTRACK" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1089, 25.06/7.39 "to": 1091, 25.06/7.39 "label": "SUCCESS" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1092, 25.06/7.39 "to": 1084, 25.06/7.39 "label": "INSTANCE with matching:\nT236 -> T250\nT238 -> T252" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1094, 25.06/7.39 "to": 1115, 25.06/7.39 "label": "SPLIT 1" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1094, 25.06/7.39 "to": 1116, 25.06/7.39 "label": "SPLIT 2\nnew knowledge:\nT271 is ground\nreplacements:T274 -> T279,\nT276 -> T280,\nT275 -> T281" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1115, 25.06/7.39 "to": 1084, 25.06/7.39 "label": "INSTANCE with matching:\nT236 -> T271\nT238 -> T274" 25.06/7.39 }, 25.06/7.39 { 25.06/7.39 "from": 1116, 25.06/7.39 "to": 873, 25.06/7.39 "label": "INSTANCE with matching:\nT179 -> .(T279, T280)\nT178 -> T281\nT19 -> T273" 25.06/7.39 } 25.06/7.39 ], 25.06/7.39 "type": "Graph" 25.06/7.39 } 25.06/7.39 } 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (156) 25.06/7.39 Complex Obligation (AND) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (157) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f1084_in(T236) -> f1086_in(T236) :|: TRUE 25.06/7.39 f1086_out(x) -> f1084_out(x) :|: TRUE 25.06/7.39 f1088_in(s(T250)) -> f1092_in(T250) :|: TRUE 25.06/7.39 f1088_in(x1) -> f1093_in :|: TRUE 25.06/7.39 f1092_out(x2) -> f1088_out(s(x2)) :|: TRUE 25.06/7.39 f1093_out -> f1088_out(x3) :|: TRUE 25.06/7.39 f1084_out(x4) -> f1092_out(x4) :|: TRUE 25.06/7.39 f1092_in(x5) -> f1084_in(x5) :|: TRUE 25.06/7.39 f1086_in(x6) -> f1087_in(x6) :|: TRUE 25.06/7.39 f1088_out(x7) -> f1086_out(x7) :|: TRUE 25.06/7.39 f1086_in(x8) -> f1088_in(x8) :|: TRUE 25.06/7.39 f1087_out(x9) -> f1086_out(x9) :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x10) -> f25_out(x10) :|: TRUE 25.06/7.39 f27_out(x11) -> f26_out(x11) :|: TRUE 25.06/7.39 f26_in(x12) -> f27_in(x12) :|: TRUE 25.06/7.39 f28_out(x13) -> f26_out(x13) :|: TRUE 25.06/7.39 f26_in(x14) -> f28_in(x14) :|: TRUE 25.06/7.39 f464_out(x15) -> f28_out(x15) :|: TRUE 25.06/7.39 f28_in(x16) -> f465_in(x16) :|: TRUE 25.06/7.39 f28_in(x17) -> f464_in(x17) :|: TRUE 25.06/7.39 f465_out(x18) -> f28_out(x18) :|: TRUE 25.06/7.39 f465_in(x19) -> f507_in :|: TRUE 25.06/7.39 f504_out(T19) -> f465_out(T19) :|: TRUE 25.06/7.39 f465_in(x20) -> f504_in(x20) :|: TRUE 25.06/7.39 f507_out -> f465_out(x21) :|: TRUE 25.06/7.39 f504_in(x22) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x23) :|: TRUE 25.06/7.39 f550_out(x24) -> f504_out(x24) :|: TRUE 25.06/7.39 f713_out -> f714_in(x25) :|: TRUE 25.06/7.39 f714_out(x26) -> f550_out(x26) :|: TRUE 25.06/7.39 f550_in(x27) -> f713_in :|: TRUE 25.06/7.39 f714_in(x28) -> f872_in :|: TRUE 25.06/7.39 f873_out(x29) -> f714_out(x29) :|: TRUE 25.06/7.39 f872_out -> f873_in(x30) :|: TRUE 25.06/7.39 f874_out(x31) -> f873_out(x31) :|: TRUE 25.06/7.39 f873_in(x32) -> f874_in(x32) :|: TRUE 25.06/7.39 f875_out(x33) -> f874_out(x33) :|: TRUE 25.06/7.39 f876_out(x34) -> f874_out(x34) :|: TRUE 25.06/7.39 f874_in(x35) -> f875_in(x35) :|: TRUE 25.06/7.39 f874_in(x36) -> f876_in(x36) :|: TRUE 25.06/7.39 f884_out(x37) -> f876_out(x37) :|: TRUE 25.06/7.39 f876_in(x38) -> f885_in(x38) :|: TRUE 25.06/7.39 f876_in(x39) -> f884_in(x39) :|: TRUE 25.06/7.39 f885_out(x40) -> f876_out(x40) :|: TRUE 25.06/7.39 f1073_out(x41) -> f885_out(x41) :|: TRUE 25.06/7.39 f885_in(x42) -> f1073_in(x42) :|: TRUE 25.06/7.39 f885_in(x43) -> f1072_in(x43) :|: TRUE 25.06/7.39 f1072_out(x44) -> f885_out(x44) :|: TRUE 25.06/7.39 f1072_in(.(T212, T216)) -> f1074_in(T212, T216) :|: TRUE 25.06/7.39 f1072_in(x45) -> f1075_in :|: TRUE 25.06/7.39 f1075_out -> f1072_out(x46) :|: TRUE 25.06/7.39 f1074_out(x47, x48) -> f1072_out(.(x47, x48)) :|: TRUE 25.06/7.39 f1074_in(x49, x50) -> f1076_in(x49) :|: TRUE 25.06/7.39 f1076_out(x51) -> f1077_in(x52) :|: TRUE 25.06/7.39 f1077_out(x53) -> f1074_out(x54, x53) :|: TRUE 25.06/7.39 f1076_in(x55) -> f1078_in(x55) :|: TRUE 25.06/7.39 f1078_out(x56) -> f1076_out(x56) :|: TRUE 25.06/7.39 f1078_in(x57) -> f1079_in(x57) :|: TRUE 25.06/7.39 f1079_out(x58) -> f1078_out(x58) :|: TRUE 25.06/7.39 f1080_out(x59) -> f1078_out(x59) :|: TRUE 25.06/7.39 f1078_in(x60) -> f1080_in(x60) :|: TRUE 25.06/7.39 f1080_in(x61) -> f1085_in :|: TRUE 25.06/7.39 f1085_out -> f1080_out(x62) :|: TRUE 25.06/7.39 f1084_out(x63) -> f1080_out(s(x63)) :|: TRUE 25.06/7.39 f1080_in(s(x64)) -> f1084_in(x64) :|: TRUE 25.06/7.39 f1095_out -> f1073_out(x65) :|: TRUE 25.06/7.39 f1094_out(T271, T273) -> f1073_out(.(T271, T273)) :|: TRUE 25.06/7.39 f1073_in(x66) -> f1095_in :|: TRUE 25.06/7.39 f1073_in(.(x67, x68)) -> f1094_in(x67, x68) :|: TRUE 25.06/7.39 f1094_in(x69, x70) -> f1115_in(x69) :|: TRUE 25.06/7.39 f1115_out(x71) -> f1116_in(x72) :|: TRUE 25.06/7.39 f1116_out(x73) -> f1094_out(x74, x73) :|: TRUE 25.06/7.39 f1115_in(x75) -> f1084_in(x75) :|: TRUE 25.06/7.39 f1084_out(x76) -> f1115_out(x76) :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (158) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (159) 25.06/7.39 TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (160) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f873_out(T216) -> f1077_out(T216) :|: TRUE 25.06/7.39 f1077_in(x) -> f873_in(x) :|: TRUE 25.06/7.39 f1082_out -> f1079_out(T212) :|: TRUE 25.06/7.39 f1079_in(0) -> f1081_in :|: TRUE 25.06/7.39 f1081_out -> f1079_out(0) :|: TRUE 25.06/7.39 f1079_in(x1) -> f1082_in :|: TRUE 25.06/7.39 f1072_in(.(x2, x3)) -> f1074_in(x2, x3) :|: TRUE 25.06/7.39 f1072_in(T19) -> f1075_in :|: TRUE 25.06/7.39 f1075_out -> f1072_out(x4) :|: TRUE 25.06/7.39 f1074_out(x5, x6) -> f1072_out(.(x5, x6)) :|: TRUE 25.06/7.39 f884_out(x7) -> f876_out(x7) :|: TRUE 25.06/7.39 f876_in(x8) -> f885_in(x8) :|: TRUE 25.06/7.39 f876_in(x9) -> f884_in(x9) :|: TRUE 25.06/7.39 f885_out(x10) -> f876_out(x10) :|: TRUE 25.06/7.39 f1078_in(x11) -> f1079_in(x11) :|: TRUE 25.06/7.39 f1079_out(x12) -> f1078_out(x12) :|: TRUE 25.06/7.39 f1080_out(x13) -> f1078_out(x13) :|: TRUE 25.06/7.39 f1078_in(x14) -> f1080_in(x14) :|: TRUE 25.06/7.39 f1116_in(T273) -> f873_in(T273) :|: TRUE 25.06/7.39 f873_out(x15) -> f1116_out(x15) :|: TRUE 25.06/7.39 f1115_in(T271) -> f1084_in(T271) :|: TRUE 25.06/7.39 f1084_out(x16) -> f1115_out(x16) :|: TRUE 25.06/7.39 f1095_out -> f1073_out(x17) :|: TRUE 25.06/7.39 f1094_out(x18, x19) -> f1073_out(.(x18, x19)) :|: TRUE 25.06/7.39 f1073_in(x20) -> f1095_in :|: TRUE 25.06/7.39 f1073_in(.(x21, x22)) -> f1094_in(x21, x22) :|: TRUE 25.06/7.39 f1088_in(s(T250)) -> f1092_in(T250) :|: TRUE 25.06/7.39 f1088_in(T236) -> f1093_in :|: TRUE 25.06/7.39 f1092_out(x23) -> f1088_out(s(x23)) :|: TRUE 25.06/7.39 f1093_out -> f1088_out(x24) :|: TRUE 25.06/7.39 f1089_in -> f1089_out :|: TRUE 25.06/7.39 f1081_in -> f1081_out :|: TRUE 25.06/7.39 f875_out(x25) -> f874_out(x25) :|: TRUE 25.06/7.39 f876_out(x26) -> f874_out(x26) :|: TRUE 25.06/7.39 f874_in(x27) -> f875_in(x27) :|: TRUE 25.06/7.39 f874_in(x28) -> f876_in(x28) :|: TRUE 25.06/7.39 f874_out(x29) -> f873_out(x29) :|: TRUE 25.06/7.39 f873_in(x30) -> f874_in(x30) :|: TRUE 25.06/7.39 f1090_out -> f1087_out(x31) :|: TRUE 25.06/7.39 f1089_out -> f1087_out(0) :|: TRUE 25.06/7.39 f1087_in(0) -> f1089_in :|: TRUE 25.06/7.39 f1087_in(x32) -> f1090_in :|: TRUE 25.06/7.39 f1076_in(x33) -> f1078_in(x33) :|: TRUE 25.06/7.39 f1078_out(x34) -> f1076_out(x34) :|: TRUE 25.06/7.39 f1084_out(x35) -> f1092_out(x35) :|: TRUE 25.06/7.39 f1092_in(x36) -> f1084_in(x36) :|: TRUE 25.06/7.39 f1074_in(x37, x38) -> f1076_in(x37) :|: TRUE 25.06/7.39 f1076_out(x39) -> f1077_in(x40) :|: TRUE 25.06/7.39 f1077_out(x41) -> f1074_out(x42, x41) :|: TRUE 25.06/7.39 f1084_in(x43) -> f1086_in(x43) :|: TRUE 25.06/7.39 f1086_out(x44) -> f1084_out(x44) :|: TRUE 25.06/7.39 f1073_out(x45) -> f885_out(x45) :|: TRUE 25.06/7.39 f885_in(x46) -> f1073_in(x46) :|: TRUE 25.06/7.39 f885_in(x47) -> f1072_in(x47) :|: TRUE 25.06/7.39 f1072_out(x48) -> f885_out(x48) :|: TRUE 25.06/7.39 f1080_in(x49) -> f1085_in :|: TRUE 25.06/7.39 f1085_out -> f1080_out(x50) :|: TRUE 25.06/7.39 f1084_out(x51) -> f1080_out(s(x51)) :|: TRUE 25.06/7.39 f1080_in(s(x52)) -> f1084_in(x52) :|: TRUE 25.06/7.39 f1086_in(x53) -> f1087_in(x53) :|: TRUE 25.06/7.39 f1088_out(x54) -> f1086_out(x54) :|: TRUE 25.06/7.39 f1086_in(x55) -> f1088_in(x55) :|: TRUE 25.06/7.39 f1087_out(x56) -> f1086_out(x56) :|: TRUE 25.06/7.39 f1094_in(x57, x58) -> f1115_in(x57) :|: TRUE 25.06/7.39 f1115_out(x59) -> f1116_in(x60) :|: TRUE 25.06/7.39 f1116_out(x61) -> f1094_out(x62, x61) :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x63) -> f25_out(x63) :|: TRUE 25.06/7.39 f27_out(x64) -> f26_out(x64) :|: TRUE 25.06/7.39 f26_in(x65) -> f27_in(x65) :|: TRUE 25.06/7.39 f28_out(x66) -> f26_out(x66) :|: TRUE 25.06/7.39 f26_in(x67) -> f28_in(x67) :|: TRUE 25.06/7.39 f464_out(x68) -> f28_out(x68) :|: TRUE 25.06/7.39 f28_in(x69) -> f465_in(x69) :|: TRUE 25.06/7.39 f28_in(x70) -> f464_in(x70) :|: TRUE 25.06/7.39 f465_out(x71) -> f28_out(x71) :|: TRUE 25.06/7.39 f465_in(x72) -> f507_in :|: TRUE 25.06/7.39 f504_out(x73) -> f465_out(x73) :|: TRUE 25.06/7.39 f465_in(x74) -> f504_in(x74) :|: TRUE 25.06/7.39 f507_out -> f465_out(x75) :|: TRUE 25.06/7.39 f504_in(x76) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x77) :|: TRUE 25.06/7.39 f550_out(x78) -> f504_out(x78) :|: TRUE 25.06/7.39 f713_out -> f714_in(x79) :|: TRUE 25.06/7.39 f714_out(x80) -> f550_out(x80) :|: TRUE 25.06/7.39 f550_in(x81) -> f713_in :|: TRUE 25.06/7.39 f714_in(x82) -> f872_in :|: TRUE 25.06/7.39 f873_out(x83) -> f714_out(x83) :|: TRUE 25.06/7.39 f872_out -> f873_in(x84) :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (161) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (162) 25.06/7.39 TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (163) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f831_in -> f835_in :|: TRUE 25.06/7.39 f834_out -> f831_out :|: TRUE 25.06/7.39 f835_out -> f831_out :|: TRUE 25.06/7.39 f831_in -> f834_in :|: TRUE 25.06/7.39 f820_in -> f831_in :|: TRUE 25.06/7.39 f831_out -> f820_out :|: TRUE 25.06/7.39 f820_out -> f846_out :|: TRUE 25.06/7.39 f846_in -> f820_in :|: TRUE 25.06/7.39 f847_out -> f835_out :|: TRUE 25.06/7.39 f846_out -> f835_out :|: TRUE 25.06/7.39 f835_in -> f846_in :|: TRUE 25.06/7.39 f835_in -> f847_in :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x) -> f25_out(x) :|: TRUE 25.06/7.39 f27_out(x1) -> f26_out(x1) :|: TRUE 25.06/7.39 f26_in(x2) -> f27_in(x2) :|: TRUE 25.06/7.39 f28_out(x3) -> f26_out(x3) :|: TRUE 25.06/7.39 f26_in(x4) -> f28_in(x4) :|: TRUE 25.06/7.39 f464_out(x5) -> f28_out(x5) :|: TRUE 25.06/7.39 f28_in(x6) -> f465_in(x6) :|: TRUE 25.06/7.39 f28_in(x7) -> f464_in(x7) :|: TRUE 25.06/7.39 f465_out(x8) -> f28_out(x8) :|: TRUE 25.06/7.39 f465_in(x9) -> f507_in :|: TRUE 25.06/7.39 f504_out(T19) -> f465_out(T19) :|: TRUE 25.06/7.39 f465_in(x10) -> f504_in(x10) :|: TRUE 25.06/7.39 f507_out -> f465_out(x11) :|: TRUE 25.06/7.39 f504_in(x12) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_out(x14) -> f504_out(x14) :|: TRUE 25.06/7.39 f713_out -> f714_in(x15) :|: TRUE 25.06/7.39 f714_out(x16) -> f550_out(x16) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f716_out -> f713_out :|: TRUE 25.06/7.39 f718_out -> f716_out :|: TRUE 25.06/7.39 f717_out -> f716_out :|: TRUE 25.06/7.39 f716_in -> f717_in :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f722_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f723_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f722_in :|: TRUE 25.06/7.39 f741_out -> f723_out :|: TRUE 25.06/7.39 f740_out -> f723_out :|: TRUE 25.06/7.39 f723_in -> f741_in :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f743_out -> f740_out :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f743_in -> f747_in :|: TRUE 25.06/7.39 f747_out -> f748_in :|: TRUE 25.06/7.39 f748_out -> f743_out :|: TRUE 25.06/7.39 f752_out -> f748_out :|: TRUE 25.06/7.39 f751_out -> f752_in :|: TRUE 25.06/7.39 f748_in -> f751_in :|: TRUE 25.06/7.39 f756_out -> f752_out :|: TRUE 25.06/7.39 f752_in -> f756_in :|: TRUE 25.06/7.39 f756_in -> f759_in :|: TRUE 25.06/7.39 f760_out -> f756_out :|: TRUE 25.06/7.39 f759_out -> f756_out :|: TRUE 25.06/7.39 f756_in -> f760_in :|: TRUE 25.06/7.39 f760_in -> f769_in :|: TRUE 25.06/7.39 f770_out -> f760_out :|: TRUE 25.06/7.39 f769_out -> f760_out :|: TRUE 25.06/7.39 f760_in -> f770_in :|: TRUE 25.06/7.39 f778_out -> f770_out :|: TRUE 25.06/7.39 f770_in -> f778_in :|: TRUE 25.06/7.39 f770_in -> f780_in :|: TRUE 25.06/7.39 f780_out -> f770_out :|: TRUE 25.06/7.39 f778_in -> f789_in :|: TRUE 25.06/7.39 f789_out -> f778_out :|: TRUE 25.06/7.39 f787_out -> f778_out :|: TRUE 25.06/7.39 f778_in -> f787_in :|: TRUE 25.06/7.39 f799_out -> f787_out :|: TRUE 25.06/7.39 f787_in -> f798_in :|: TRUE 25.06/7.39 f798_out -> f799_in :|: TRUE 25.06/7.39 f798_in -> f800_in :|: TRUE 25.06/7.39 f800_out -> f798_out :|: TRUE 25.06/7.39 f800_in -> f803_in :|: TRUE 25.06/7.39 f803_out -> f800_out :|: TRUE 25.06/7.39 f804_out -> f800_out :|: TRUE 25.06/7.39 f800_in -> f804_in :|: TRUE 25.06/7.39 f820_out -> f804_out :|: TRUE 25.06/7.39 f823_out -> f804_out :|: TRUE 25.06/7.39 f804_in -> f820_in :|: TRUE 25.06/7.39 f804_in -> f823_in :|: TRUE 25.06/7.39 f861_out -> f780_out :|: TRUE 25.06/7.39 f860_out -> f780_out :|: TRUE 25.06/7.39 f780_in -> f861_in :|: TRUE 25.06/7.39 f780_in -> f860_in :|: TRUE 25.06/7.39 f860_in -> f865_in :|: TRUE 25.06/7.39 f865_out -> f866_in :|: TRUE 25.06/7.39 f866_out -> f860_out :|: TRUE 25.06/7.39 f820_out -> f865_out :|: TRUE 25.06/7.39 f865_in -> f820_in :|: TRUE 25.06/7.39 f714_in(x18) -> f872_in :|: TRUE 25.06/7.39 f873_out(x19) -> f714_out(x19) :|: TRUE 25.06/7.39 f872_out -> f873_in(x20) :|: TRUE 25.06/7.39 f872_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f872_out :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (164) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (165) 25.06/7.39 TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (166) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f778_in -> f789_in :|: TRUE 25.06/7.39 f789_out -> f778_out :|: TRUE 25.06/7.39 f787_out -> f778_out :|: TRUE 25.06/7.39 f778_in -> f787_in :|: TRUE 25.06/7.39 f812_in -> f812_out :|: TRUE 25.06/7.39 f752_out -> f799_out :|: TRUE 25.06/7.39 f799_in -> f752_in :|: TRUE 25.06/7.39 f756_out -> f752_out :|: TRUE 25.06/7.39 f752_in -> f756_in :|: TRUE 25.06/7.39 f800_in -> f803_in :|: TRUE 25.06/7.39 f803_out -> f800_out :|: TRUE 25.06/7.39 f804_out -> f800_out :|: TRUE 25.06/7.39 f800_in -> f804_in :|: TRUE 25.06/7.39 f778_out -> f770_out :|: TRUE 25.06/7.39 f770_in -> f778_in :|: TRUE 25.06/7.39 f770_in -> f780_in :|: TRUE 25.06/7.39 f780_out -> f770_out :|: TRUE 25.06/7.39 f834_in -> f842_in :|: TRUE 25.06/7.39 f842_out -> f834_out :|: TRUE 25.06/7.39 f840_out -> f834_out :|: TRUE 25.06/7.39 f834_in -> f840_in :|: TRUE 25.06/7.39 f752_out -> f866_out :|: TRUE 25.06/7.39 f866_in -> f752_in :|: TRUE 25.06/7.39 f799_out -> f787_out :|: TRUE 25.06/7.39 f787_in -> f798_in :|: TRUE 25.06/7.39 f798_out -> f799_in :|: TRUE 25.06/7.39 f760_in -> f769_in :|: TRUE 25.06/7.39 f770_out -> f760_out :|: TRUE 25.06/7.39 f769_out -> f760_out :|: TRUE 25.06/7.39 f760_in -> f770_in :|: TRUE 25.06/7.39 f840_in -> f840_out :|: TRUE 25.06/7.39 f820_out -> f846_out :|: TRUE 25.06/7.39 f846_in -> f820_in :|: TRUE 25.06/7.39 f756_in -> f759_in :|: TRUE 25.06/7.39 f760_out -> f756_out :|: TRUE 25.06/7.39 f759_out -> f756_out :|: TRUE 25.06/7.39 f756_in -> f760_in :|: TRUE 25.06/7.39 f798_in -> f800_in :|: TRUE 25.06/7.39 f800_out -> f798_out :|: TRUE 25.06/7.39 f820_out -> f865_out :|: TRUE 25.06/7.39 f865_in -> f820_in :|: TRUE 25.06/7.39 f813_out -> f803_out :|: TRUE 25.06/7.39 f812_out -> f803_out :|: TRUE 25.06/7.39 f803_in -> f813_in :|: TRUE 25.06/7.39 f803_in -> f812_in :|: TRUE 25.06/7.39 f847_out -> f835_out :|: TRUE 25.06/7.39 f846_out -> f835_out :|: TRUE 25.06/7.39 f835_in -> f846_in :|: TRUE 25.06/7.39 f835_in -> f847_in :|: TRUE 25.06/7.39 f831_in -> f835_in :|: TRUE 25.06/7.39 f834_out -> f831_out :|: TRUE 25.06/7.39 f835_out -> f831_out :|: TRUE 25.06/7.39 f831_in -> f834_in :|: TRUE 25.06/7.39 f820_in -> f831_in :|: TRUE 25.06/7.39 f831_out -> f820_out :|: TRUE 25.06/7.39 f860_in -> f865_in :|: TRUE 25.06/7.39 f865_out -> f866_in :|: TRUE 25.06/7.39 f866_out -> f860_out :|: TRUE 25.06/7.39 f861_out -> f780_out :|: TRUE 25.06/7.39 f860_out -> f780_out :|: TRUE 25.06/7.39 f780_in -> f861_in :|: TRUE 25.06/7.39 f780_in -> f860_in :|: TRUE 25.06/7.39 f820_out -> f804_out :|: TRUE 25.06/7.39 f823_out -> f804_out :|: TRUE 25.06/7.39 f804_in -> f820_in :|: TRUE 25.06/7.39 f804_in -> f823_in :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x) -> f25_out(x) :|: TRUE 25.06/7.39 f27_out(x1) -> f26_out(x1) :|: TRUE 25.06/7.39 f26_in(x2) -> f27_in(x2) :|: TRUE 25.06/7.39 f28_out(x3) -> f26_out(x3) :|: TRUE 25.06/7.39 f26_in(x4) -> f28_in(x4) :|: TRUE 25.06/7.39 f464_out(x5) -> f28_out(x5) :|: TRUE 25.06/7.39 f28_in(x6) -> f465_in(x6) :|: TRUE 25.06/7.39 f28_in(x7) -> f464_in(x7) :|: TRUE 25.06/7.39 f465_out(x8) -> f28_out(x8) :|: TRUE 25.06/7.39 f465_in(x9) -> f507_in :|: TRUE 25.06/7.39 f504_out(T19) -> f465_out(T19) :|: TRUE 25.06/7.39 f465_in(x10) -> f504_in(x10) :|: TRUE 25.06/7.39 f507_out -> f465_out(x11) :|: TRUE 25.06/7.39 f504_in(x12) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_out(x14) -> f504_out(x14) :|: TRUE 25.06/7.39 f713_out -> f714_in(x15) :|: TRUE 25.06/7.39 f714_out(x16) -> f550_out(x16) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 f714_in(x18) -> f872_in :|: TRUE 25.06/7.39 f873_out(x19) -> f714_out(x19) :|: TRUE 25.06/7.39 f872_out -> f873_in(x20) :|: TRUE 25.06/7.39 f872_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f872_out :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f716_out -> f713_out :|: TRUE 25.06/7.39 f718_out -> f716_out :|: TRUE 25.06/7.39 f717_out -> f716_out :|: TRUE 25.06/7.39 f716_in -> f717_in :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f722_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f723_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f722_in :|: TRUE 25.06/7.39 f741_out -> f723_out :|: TRUE 25.06/7.39 f740_out -> f723_out :|: TRUE 25.06/7.39 f723_in -> f741_in :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f743_out -> f740_out :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f743_in -> f747_in :|: TRUE 25.06/7.39 f747_out -> f748_in :|: TRUE 25.06/7.39 f748_out -> f743_out :|: TRUE 25.06/7.39 f752_out -> f748_out :|: TRUE 25.06/7.39 f751_out -> f752_in :|: TRUE 25.06/7.39 f748_in -> f751_in :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (167) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (168) 25.06/7.39 TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (169) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f639_out :|: TRUE 25.06/7.39 f599_out -> f594_out :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_out -> f599_out :|: TRUE 25.06/7.39 f599_in -> f603_in :|: TRUE 25.06/7.39 f603_out -> f599_out :|: TRUE 25.06/7.39 f639_out -> f605_out :|: TRUE 25.06/7.39 f643_out -> f605_out :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 f605_in -> f643_in :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x) -> f25_out(x) :|: TRUE 25.06/7.39 f27_out(x1) -> f26_out(x1) :|: TRUE 25.06/7.39 f26_in(x2) -> f27_in(x2) :|: TRUE 25.06/7.39 f28_out(x3) -> f26_out(x3) :|: TRUE 25.06/7.39 f26_in(x4) -> f28_in(x4) :|: TRUE 25.06/7.39 f464_out(x5) -> f28_out(x5) :|: TRUE 25.06/7.39 f28_in(x6) -> f465_in(x6) :|: TRUE 25.06/7.39 f28_in(x7) -> f464_in(x7) :|: TRUE 25.06/7.39 f465_out(x8) -> f28_out(x8) :|: TRUE 25.06/7.39 f465_in(x9) -> f507_in :|: TRUE 25.06/7.39 f504_out(T19) -> f465_out(T19) :|: TRUE 25.06/7.39 f465_in(x10) -> f504_in(x10) :|: TRUE 25.06/7.39 f507_out -> f465_out(x11) :|: TRUE 25.06/7.39 f504_in(x12) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_out(x14) -> f504_out(x14) :|: TRUE 25.06/7.39 f713_out -> f714_in(x15) :|: TRUE 25.06/7.39 f714_out(x16) -> f550_out(x16) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 f714_in(x18) -> f872_in :|: TRUE 25.06/7.39 f873_out(x19) -> f714_out(x19) :|: TRUE 25.06/7.39 f872_out -> f873_in(x20) :|: TRUE 25.06/7.39 f872_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f872_out :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f716_out -> f713_out :|: TRUE 25.06/7.39 f718_out -> f716_out :|: TRUE 25.06/7.39 f717_out -> f716_out :|: TRUE 25.06/7.39 f716_in -> f717_in :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f722_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f723_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f722_in :|: TRUE 25.06/7.39 f741_out -> f723_out :|: TRUE 25.06/7.39 f740_out -> f723_out :|: TRUE 25.06/7.39 f723_in -> f741_in :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f743_out -> f740_out :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f742_in -> f549_in :|: TRUE 25.06/7.39 f549_out -> f742_out :|: TRUE 25.06/7.39 f549_in -> f551_in :|: TRUE 25.06/7.39 f551_out -> f549_out :|: TRUE 25.06/7.39 f551_in -> f552_in :|: TRUE 25.06/7.39 f552_out -> f551_out :|: TRUE 25.06/7.39 f552_in -> f559_in :|: TRUE 25.06/7.39 f559_out -> f552_out :|: TRUE 25.06/7.39 f565_out -> f559_out :|: TRUE 25.06/7.39 f559_in -> f565_in :|: TRUE 25.06/7.39 f566_out -> f565_out :|: TRUE 25.06/7.39 f565_in -> f566_in :|: TRUE 25.06/7.39 f566_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f566_out :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (170) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 intTRSProblem: 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (171) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (172) IntTRSCompressionProof (EQUIVALENT) 25.06/7.39 Compressed rules. 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (173) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f639_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (174) IRSFormatTransformerProof (EQUIVALENT) 25.06/7.39 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (175) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f639_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (176) IRSwTTerminationDigraphProof (EQUIVALENT) 25.06/7.39 Constructed termination digraph! 25.06/7.39 Nodes: 25.06/7.39 (1) f639_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 Arcs: 25.06/7.39 (1) -> (1) 25.06/7.39 25.06/7.39 This digraph is fully evaluated! 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (177) 25.06/7.39 Obligation: 25.06/7.39 25.06/7.39 Termination digraph: 25.06/7.39 Nodes: 25.06/7.39 (1) f639_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 Arcs: 25.06/7.39 (1) -> (1) 25.06/7.39 25.06/7.39 This digraph is fully evaluated! 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (178) FilterProof (EQUIVALENT) 25.06/7.39 Used the following sort dictionary for filtering: 25.06/7.39 f639_in() 25.06/7.39 Replaced non-predefined constructor symbols by 0. 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (179) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f639_in -> f639_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (180) IntTRSNonPeriodicNontermProof (COMPLETE) 25.06/7.39 Normalized system to the following form: 25.06/7.39 f(pc) -> f(1) :|: pc = 1 && TRUE 25.06/7.39 Proved unsatisfiability of the following formula, indicating that the system is never left after entering: 25.06/7.39 ((run2_0 = ((1 * 1)) and (((run1_0 * 1)) = ((1 * 1)) and T)) and !(((run2_0 * 1)) = ((1 * 1)) and T)) 25.06/7.39 Proved satisfiability of the following formula, indicating that the system is entered at least once: 25.06/7.39 (run2_0 = ((1 * 1)) and (((run1_0 * 1)) = ((1 * 1)) and T)) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (181) 25.06/7.39 NO 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (182) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f778_in -> f789_in :|: TRUE 25.06/7.39 f789_out -> f778_out :|: TRUE 25.06/7.39 f787_out -> f778_out :|: TRUE 25.06/7.39 f778_in -> f787_in :|: TRUE 25.06/7.39 f812_in -> f812_out :|: TRUE 25.06/7.39 f752_out -> f799_out :|: TRUE 25.06/7.39 f799_in -> f752_in :|: TRUE 25.06/7.39 f800_in -> f803_in :|: TRUE 25.06/7.39 f803_out -> f800_out :|: TRUE 25.06/7.39 f804_out -> f800_out :|: TRUE 25.06/7.39 f800_in -> f804_in :|: TRUE 25.06/7.39 f549_in -> f551_in :|: TRUE 25.06/7.39 f551_out -> f549_out :|: TRUE 25.06/7.39 f751_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f751_out :|: TRUE 25.06/7.39 f752_out -> f866_out :|: TRUE 25.06/7.39 f866_in -> f752_in :|: TRUE 25.06/7.39 f764_in -> f764_out :|: TRUE 25.06/7.39 f743_in -> f747_in :|: TRUE 25.06/7.39 f747_out -> f748_in :|: TRUE 25.06/7.39 f748_out -> f743_out :|: TRUE 25.06/7.39 f769_in -> f774_in :|: TRUE 25.06/7.39 f769_in -> f775_in :|: TRUE 25.06/7.39 f775_out -> f769_out :|: TRUE 25.06/7.39 f774_out -> f769_out :|: TRUE 25.06/7.39 f722_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f723_out -> f718_out :|: TRUE 25.06/7.39 f718_in -> f722_in :|: TRUE 25.06/7.39 f799_out -> f787_out :|: TRUE 25.06/7.39 f787_in -> f798_in :|: TRUE 25.06/7.39 f798_out -> f799_in :|: TRUE 25.06/7.39 f743_out -> f740_out :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f551_in -> f552_in :|: TRUE 25.06/7.39 f552_out -> f551_out :|: TRUE 25.06/7.39 f760_in -> f769_in :|: TRUE 25.06/7.39 f770_out -> f760_out :|: TRUE 25.06/7.39 f769_out -> f760_out :|: TRUE 25.06/7.39 f760_in -> f770_in :|: TRUE 25.06/7.39 f840_in -> f840_out :|: TRUE 25.06/7.39 f798_in -> f800_in :|: TRUE 25.06/7.39 f800_out -> f798_out :|: TRUE 25.06/7.39 f820_out -> f865_out :|: TRUE 25.06/7.39 f865_in -> f820_in :|: TRUE 25.06/7.39 f813_out -> f803_out :|: TRUE 25.06/7.39 f812_out -> f803_out :|: TRUE 25.06/7.39 f803_in -> f813_in :|: TRUE 25.06/7.39 f803_in -> f812_in :|: TRUE 25.06/7.39 f718_out -> f716_out :|: TRUE 25.06/7.39 f717_out -> f716_out :|: TRUE 25.06/7.39 f716_in -> f717_in :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f847_out -> f835_out :|: TRUE 25.06/7.39 f846_out -> f835_out :|: TRUE 25.06/7.39 f835_in -> f846_in :|: TRUE 25.06/7.39 f835_in -> f847_in :|: TRUE 25.06/7.39 f820_in -> f831_in :|: TRUE 25.06/7.39 f831_out -> f820_out :|: TRUE 25.06/7.39 f860_in -> f865_in :|: TRUE 25.06/7.39 f865_out -> f866_in :|: TRUE 25.06/7.39 f866_out -> f860_out :|: TRUE 25.06/7.39 f774_in -> f774_out :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_out -> f599_out :|: TRUE 25.06/7.39 f599_in -> f603_in :|: TRUE 25.06/7.39 f603_out -> f599_out :|: TRUE 25.06/7.39 f756_out -> f752_out :|: TRUE 25.06/7.39 f752_in -> f756_in :|: TRUE 25.06/7.39 f552_in -> f559_in :|: TRUE 25.06/7.39 f559_out -> f552_out :|: TRUE 25.06/7.39 f778_out -> f770_out :|: TRUE 25.06/7.39 f770_in -> f778_in :|: TRUE 25.06/7.39 f770_in -> f780_in :|: TRUE 25.06/7.39 f780_out -> f770_out :|: TRUE 25.06/7.39 f834_in -> f842_in :|: TRUE 25.06/7.39 f842_out -> f834_out :|: TRUE 25.06/7.39 f840_out -> f834_out :|: TRUE 25.06/7.39 f834_in -> f840_in :|: TRUE 25.06/7.39 f565_out -> f559_out :|: TRUE 25.06/7.39 f559_in -> f565_in :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f716_out -> f713_out :|: TRUE 25.06/7.39 f566_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f566_out :|: TRUE 25.06/7.39 f752_out -> f748_out :|: TRUE 25.06/7.39 f751_out -> f752_in :|: TRUE 25.06/7.39 f748_in -> f751_in :|: TRUE 25.06/7.39 f741_out -> f723_out :|: TRUE 25.06/7.39 f740_out -> f723_out :|: TRUE 25.06/7.39 f723_in -> f741_in :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f611_out -> f603_out :|: TRUE 25.06/7.39 f603_in -> f614_in :|: TRUE 25.06/7.39 f603_in -> f611_in :|: TRUE 25.06/7.39 f614_out -> f603_out :|: TRUE 25.06/7.39 f599_out -> f594_out :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f820_out -> f846_out :|: TRUE 25.06/7.39 f846_in -> f820_in :|: TRUE 25.06/7.39 f756_in -> f759_in :|: TRUE 25.06/7.39 f760_out -> f756_out :|: TRUE 25.06/7.39 f759_out -> f756_out :|: TRUE 25.06/7.39 f756_in -> f760_in :|: TRUE 25.06/7.39 f759_in -> f764_in :|: TRUE 25.06/7.39 f759_in -> f767_in :|: TRUE 25.06/7.39 f764_out -> f759_out :|: TRUE 25.06/7.39 f767_out -> f759_out :|: TRUE 25.06/7.39 f639_out -> f605_out :|: TRUE 25.06/7.39 f643_out -> f605_out :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 f605_in -> f643_in :|: TRUE 25.06/7.39 f831_in -> f835_in :|: TRUE 25.06/7.39 f834_out -> f831_out :|: TRUE 25.06/7.39 f835_out -> f831_out :|: TRUE 25.06/7.39 f831_in -> f834_in :|: TRUE 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f639_out :|: TRUE 25.06/7.39 f611_in -> f611_out :|: TRUE 25.06/7.39 f566_out -> f565_out :|: TRUE 25.06/7.39 f565_in -> f566_in :|: TRUE 25.06/7.39 f747_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f747_out :|: TRUE 25.06/7.39 f742_in -> f549_in :|: TRUE 25.06/7.39 f549_out -> f742_out :|: TRUE 25.06/7.39 f861_out -> f780_out :|: TRUE 25.06/7.39 f860_out -> f780_out :|: TRUE 25.06/7.39 f780_in -> f861_in :|: TRUE 25.06/7.39 f780_in -> f860_in :|: TRUE 25.06/7.39 f820_out -> f804_out :|: TRUE 25.06/7.39 f823_out -> f804_out :|: TRUE 25.06/7.39 f804_in -> f820_in :|: TRUE 25.06/7.39 f804_in -> f823_in :|: TRUE 25.06/7.39 f25_in(T2) -> f26_in(T2) :|: TRUE 25.06/7.39 f26_out(x) -> f25_out(x) :|: TRUE 25.06/7.39 f27_out(x1) -> f26_out(x1) :|: TRUE 25.06/7.39 f26_in(x2) -> f27_in(x2) :|: TRUE 25.06/7.39 f28_out(x3) -> f26_out(x3) :|: TRUE 25.06/7.39 f26_in(x4) -> f28_in(x4) :|: TRUE 25.06/7.39 f464_out(x5) -> f28_out(x5) :|: TRUE 25.06/7.39 f28_in(x6) -> f465_in(x6) :|: TRUE 25.06/7.39 f28_in(x7) -> f464_in(x7) :|: TRUE 25.06/7.39 f465_out(x8) -> f28_out(x8) :|: TRUE 25.06/7.39 f465_in(x9) -> f507_in :|: TRUE 25.06/7.39 f504_out(T19) -> f465_out(T19) :|: TRUE 25.06/7.39 f465_in(x10) -> f504_in(x10) :|: TRUE 25.06/7.39 f507_out -> f465_out(x11) :|: TRUE 25.06/7.39 f504_in(x12) -> f549_in :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_out(x14) -> f504_out(x14) :|: TRUE 25.06/7.39 f713_out -> f714_in(x15) :|: TRUE 25.06/7.39 f714_out(x16) -> f550_out(x16) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 f714_in(x18) -> f872_in :|: TRUE 25.06/7.39 f873_out(x19) -> f714_out(x19) :|: TRUE 25.06/7.39 f872_out -> f873_in(x20) :|: TRUE 25.06/7.39 f872_in -> f713_in :|: TRUE 25.06/7.39 f713_out -> f872_out :|: TRUE 25.06/7.39 Start term: f25_in(T2) 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (183) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 25.06/7.39 Constructed simple dependency graph. 25.06/7.39 25.06/7.39 Simplified to the following IRSwTs: 25.06/7.39 25.06/7.39 intTRSProblem: 25.06/7.39 f549_in -> f551_in :|: TRUE 25.06/7.39 f551_out -> f549_out :|: TRUE 25.06/7.39 f743_in -> f747_in :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f551_in -> f552_in :|: TRUE 25.06/7.39 f552_out -> f551_out :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_out -> f599_out :|: TRUE 25.06/7.39 f599_in -> f603_in :|: TRUE 25.06/7.39 f603_out -> f599_out :|: TRUE 25.06/7.39 f552_in -> f559_in :|: TRUE 25.06/7.39 f559_out -> f552_out :|: TRUE 25.06/7.39 f565_out -> f559_out :|: TRUE 25.06/7.39 f559_in -> f565_in :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f566_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f566_out :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f611_out -> f603_out :|: TRUE 25.06/7.39 f603_in -> f611_in :|: TRUE 25.06/7.39 f599_out -> f594_out :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f639_out -> f605_out :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f639_out :|: TRUE 25.06/7.39 f611_in -> f611_out :|: TRUE 25.06/7.39 f566_out -> f565_out :|: TRUE 25.06/7.39 f565_in -> f566_in :|: TRUE 25.06/7.39 f747_in -> f713_in :|: TRUE 25.06/7.39 f742_in -> f549_in :|: TRUE 25.06/7.39 f549_out -> f742_out :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (184) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f549_in -> f551_in :|: TRUE 25.06/7.39 f551_out -> f549_out :|: TRUE 25.06/7.39 f743_in -> f747_in :|: TRUE 25.06/7.39 f718_in -> f723_in :|: TRUE 25.06/7.39 f740_in -> f742_in :|: TRUE 25.06/7.39 f742_out -> f743_in :|: TRUE 25.06/7.39 f551_in -> f552_in :|: TRUE 25.06/7.39 f552_out -> f551_out :|: TRUE 25.06/7.39 f716_in -> f718_in :|: TRUE 25.06/7.39 f599_in -> f605_in :|: TRUE 25.06/7.39 f605_out -> f599_out :|: TRUE 25.06/7.39 f599_in -> f603_in :|: TRUE 25.06/7.39 f603_out -> f599_out :|: TRUE 25.06/7.39 f552_in -> f559_in :|: TRUE 25.06/7.39 f559_out -> f552_out :|: TRUE 25.06/7.39 f565_out -> f559_out :|: TRUE 25.06/7.39 f559_in -> f565_in :|: TRUE 25.06/7.39 f713_in -> f716_in :|: TRUE 25.06/7.39 f566_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f566_out :|: TRUE 25.06/7.39 f723_in -> f740_in :|: TRUE 25.06/7.39 f611_out -> f603_out :|: TRUE 25.06/7.39 f603_in -> f611_in :|: TRUE 25.06/7.39 f599_out -> f594_out :|: TRUE 25.06/7.39 f594_in -> f599_in :|: TRUE 25.06/7.39 f639_out -> f605_out :|: TRUE 25.06/7.39 f605_in -> f639_in :|: TRUE 25.06/7.39 f639_in -> f594_in :|: TRUE 25.06/7.39 f594_out -> f639_out :|: TRUE 25.06/7.39 f611_in -> f611_out :|: TRUE 25.06/7.39 f566_out -> f565_out :|: TRUE 25.06/7.39 f565_in -> f566_in :|: TRUE 25.06/7.39 f747_in -> f713_in :|: TRUE 25.06/7.39 f742_in -> f549_in :|: TRUE 25.06/7.39 f549_out -> f742_out :|: TRUE 25.06/7.39 f549_out -> f550_in(x13) :|: TRUE 25.06/7.39 f550_in(x17) -> f713_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (185) IntTRSCompressionProof (EQUIVALENT) 25.06/7.39 Compressed rules. 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (186) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f594_out -> f594_out :|: TRUE 25.06/7.39 f594_out -> f599_in :|: TRUE 25.06/7.39 f599_in -> f599_in :|: TRUE 25.06/7.39 f599_in -> f594_out :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (187) IRSFormatTransformerProof (EQUIVALENT) 25.06/7.39 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (188) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f594_out -> f594_out :|: TRUE 25.06/7.39 f594_out -> f599_in :|: TRUE 25.06/7.39 f599_in -> f599_in :|: TRUE 25.06/7.39 f599_in -> f594_out :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (189) IRSwTTerminationDigraphProof (EQUIVALENT) 25.06/7.39 Constructed termination digraph! 25.06/7.39 Nodes: 25.06/7.39 (1) f594_out -> f594_out :|: TRUE 25.06/7.39 (2) f594_out -> f599_in :|: TRUE 25.06/7.39 (3) f599_in -> f599_in :|: TRUE 25.06/7.39 (4) f599_in -> f594_out :|: TRUE 25.06/7.39 25.06/7.39 Arcs: 25.06/7.39 (1) -> (1), (2) 25.06/7.39 (2) -> (3), (4) 25.06/7.39 (3) -> (3), (4) 25.06/7.39 (4) -> (1), (2) 25.06/7.39 25.06/7.39 This digraph is fully evaluated! 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (190) 25.06/7.39 Obligation: 25.06/7.39 25.06/7.39 Termination digraph: 25.06/7.39 Nodes: 25.06/7.39 (1) f594_out -> f594_out :|: TRUE 25.06/7.39 (2) f599_in -> f594_out :|: TRUE 25.06/7.39 (3) f599_in -> f599_in :|: TRUE 25.06/7.39 (4) f594_out -> f599_in :|: TRUE 25.06/7.39 25.06/7.39 Arcs: 25.06/7.39 (1) -> (1), (4) 25.06/7.39 (2) -> (1), (4) 25.06/7.39 (3) -> (2), (3) 25.06/7.39 (4) -> (2), (3) 25.06/7.39 25.06/7.39 This digraph is fully evaluated! 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (191) FilterProof (EQUIVALENT) 25.06/7.39 Used the following sort dictionary for filtering: 25.06/7.39 f594_out() 25.06/7.39 f599_in() 25.06/7.39 Replaced non-predefined constructor symbols by 0. 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (192) 25.06/7.39 Obligation: 25.06/7.39 Rules: 25.06/7.39 f594_out -> f594_out :|: TRUE 25.06/7.39 f599_in -> f594_out :|: TRUE 25.06/7.39 f599_in -> f599_in :|: TRUE 25.06/7.39 f594_out -> f599_in :|: TRUE 25.06/7.39 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (193) IntTRSPeriodicNontermProof (COMPLETE) 25.06/7.39 Normalized system to the following form: 25.06/7.39 f(pc) -> f(1) :|: pc = 1 && TRUE 25.06/7.39 f(pc) -> f(1) :|: pc = 2 && TRUE 25.06/7.39 f(pc) -> f(2) :|: pc = 2 && TRUE 25.06/7.39 f(pc) -> f(2) :|: pc = 1 && TRUE 25.06/7.39 Witness term starting non-terminating reduction: f(2) 25.06/7.39 ---------------------------------------- 25.06/7.39 25.06/7.39 (194) 25.06/7.39 NO 25.06/7.45 EOF